





























































































































































































Class ~T 3 5 3 

Ai3 


Book 


c. & 


COPYRIGHT DEPOSHV 







f 


* 




























LARGE BLACKBOARD USED IN THE DRAWING ROOM OF THE NEWTON MACHINE 

TOOL WORKS. 























Mechanical Drawing 


A Practical Manual of 

SELF-INSTRUCTION IN THE ART OF DRAFTING, LETTERING, AND RE¬ 
PRODUCING PLANS AND WORKING DRAWINGS, WITH 
ABUNDANT EXERCISES AND PLATES 


By ERVIN KENISON, S.B. 

Instructor in Mechanical Drawing, Massachusetts Institute of Technology, 

Boston, Mass. 


ILLUSTRATED 



CHICAGO 

AMERICAN SCHOOL OF CORRESPONDENCE 
M 1908 




LIBRARY of CONGRESSJ 
Two Copies Receive^ 

NOV 29 I90? 

Coyynsni tniry 
CLASS Ar tfXc. No. | 
COPY 


T3J"3 

.R53 

QsiPfVV^ 2 . 


Copyright 1907 by 

American Schooe of Correspondence 

Entered at Stationers’ Hall, Eondon 
All Rights Reserved 





Foreword 



N recent ypars, such marvelous advances have been 
made in the engineering and scientific fields, and 
so rapid has been the evolution of mechanical and 
constructive processes and methods, that a distinct 
need has been created for a series of practical 
working guides, of convenient size and low cost, embodying the 
accumulated -results of experience and the most approved modern 
practice along a great variety of lines. To fill this acknowledged 
need, is the special purpose of the series of handbooks to which 
this volume belongs. 


«L In the preparation of this series, it has been the aim of the pub¬ 
lishers to lay special stress on the practical side of each subject, 
as distinguished from mere theoretical or academic discussion. 
Each volume is written by a well-known expert of acknowledged 
authority in his special line, and is based on a most careful study 
of practical needs and up-to-date methods as developed under the 
conditions of actual practice in the field, the shop, the mill, the 
power house, the drafting room, the engine room, etc. 

C, These volumes are especially adapted for purposes of self- 
instruction and home study. The utmost care has been used to 
bring the treatment of each subject within the range of the com- 




mon understanding, so that the work will appeal not only to the 
technically trained expert, but also to the beginner and the self- 
taught practical man who wishes to keep abreast of modern 
progress. The language is simple and clear; heavy technical terms 
and the formulae of the higher mathematics have been avoided, 
yet without sacrificing any of the requirements of practical 
instruction; the arrangement of matter is such as to carry the 
reader along by easy steps to complete mastery of each subject; 
frequent examples for practice are given, to enable the reader to 
test his knowledge and make it a permanent possession; and the 
illustrations are selected with the greatest care to supplement and 
make clear the references in the text. 

<L The method adopted in the preparation of these volumes is that 
which the American School of Correspondence has developed and 
employed so successfully for many years. It is not an experiment, 
but has stood the severest of all tests—that of practical use—which 
has demonstrated it to be the best method yet devised for the 
education of the busy working man. 

<L For purposes of ready reference and timely information wdien 
needed, it is believed that this series of handbooks will be found to 
meet every requirement. 




Table of Contents 




Instruments and Materials. Page 3 

Drawing Paper— Drawing Board—Thumb Tacks—Pencils and Erasers 
—T-Square— Triangles —Compasses—Dividers—Bow Pen and Bow 
Pencil— Drawing Pen—Ink—Scales—Protractor—French or Irregular 
Curve —Beam Compasses—Lettering. 


Geometrical Definitions. Page 39 

Points — Lines—Angles — Surface's — Triangles — Quadrilaterals— 
Polygons—Circles—Measurement of Angles—Solids—Polyhedron— 
Prism—Pyramid—Cylinder—Cone—Sphere—Conic Sections (Ellipse, 
Parabola, Hyperbola, Rectangular Hyperbola)—Odontoidal Curves 
(Cycloid, Epicycloid, Hypocycloid, Involute). 

Geometrical Problems. Page 53 

To Bisect a Given Straight Line—To Construct an Angle Equal to a 
Given Angle—To Draw through a Given Point a Line Parallel to a 
Given Line—To Draw a Perpendicular to a Line from a Point There¬ 
in—To Draw a Perpendicular to a Line from a Point without It—To 
Bisect a Given Angle—To Divide a Given Line into Any Number of 
Equal Parts—To Construct a Triangle, Having Given the Three Sides; 
Having Given One Side and Two Adjacent Angles—To Describe an 
Arc or Circumference through Three Given Points Not in the Same 
Straight Line—To Inscribe a Circle in a Given Triangle; a Regular 
Pentagon or Hexagon in a Given Circle—To Draw a Line Tangent 
to a Circle at a Given Point on the Circumference; also from a Point 
outside the Circle—To Draw an Ellipse, Spiral, Parabola, Hyperbola— 

To Construct a Cycloid, Epicycloid, Hypocycloid—To Draw an In¬ 
volute. 


Projections. Page 69 

Orthographic Projection—Profile Plane—Shade Lines—Intersections— 
Developments—Isometric Projection—Oblique Projection-^Line Shad¬ 
ing—Lettering—Tracing—Blue-Printing—Assembly Drawing. 


Index 


Page 139 







A TYPICAL WORKING DRAWING 














































































































































































































































































































































MECHANICAL DRAWING 

PART I 


The subject of mechanical drawing is of great interest and 
importance to all mechanics and engineers. Drawing is the 
method used to show graphically the small details of machinery; 
it is the language by which the designer speaks to the workman; 
it is the most graphical way to place ideas and calculations on 
record. Working drawings take the place of lengthy explana¬ 
tions, either written or verbal. A brief inspection of an accurate, 
well-executed drawing gives a better idea of a machine than a 
large amount of verbal description. The better and more clearly 
a drawing is made, the more intelligently the workman can com¬ 
prehend the ideas of the designer. A thorough training in this 
important subject is necessary to the success of everyone engaged 
in mechanical work. The success of a draftsman depends to some 
extent upon the quality of his instruments and materials. Begin¬ 
ners frequently purchase a cheap grade of instruments. After 
they have become expert and have learned to take care of their 
instruments they discard them for those of better construction and 
finish. This plan has its advantages, but to do the best work, 
strong, well-made and finely finished instillments are necessary. 

INSTRUMENTS AND MATERIALS. 

Drawing Paper. In selecting drawing paper, the first thing 
to be considered is the kind of paper most suitable for the pro¬ 
posed work. For shop drawings, a manilla paper is frequently 
used, on account of its toughness and strength, because the draw¬ 
ing is likely to be subjected to considerable hard usage. If a 
finished drawing is to be made, the best white drawing paper 
should be obtained, so that the drawing will not fade or become 
discolored with age. A good drawing paper' should be strong, 
have uniform thickness and surface, should stretch evenly, and 
should neither repel nor absorb liquids. It should also allow con¬ 
siderable erasing without spoiling the surface, and it should lie 
smooth when stretched or when ink or colors are used. It is, of 



4 


MECHANICAL DRAWING 


course, impossible to find all of these qualities in any one paper, 
as for instance great strength cannot be combined with fine 
surface. 

In selecting a drawing paper the kind should be chosen 
which combines the greatest number of these qualities for the 
given work. Of the better class Whatman’s are considered by 
far the best. This paper is made in three grades; the hot 
'pressed has a smooth surface and is especially adapted for pencil 
and very fine line drawing, the cold pressed is rougher than 
the hot pressed, has a finely grained surface and is more suit¬ 
able for water color drawing; the rough is used for tinting. The 
cold pressed does not take ink as well as the hot pressed, but 
erasures do not show as much on it, and it is better for general 
work. There is but little difference in the two sides of Whatman’s 
paper, and either can be used. This paper comes in sheets of 
standard sizes as follows:— 


Cap, 

Demy, 

Medium, 

Royal, 

Super-Royal, 

Imperial, 


13 X 17 inches. 
15 X 20 “ 

17 X 22 “ 

19 X 24 “ 

19 X 27 “ 

22 X 30 “ 


Elephant, 

Columbia, 

Atlas, 

Double Elephant, 

Antiquarian, 

Emperor, 


23 X 28 inches. 

23 X 34 “ 

26 X 34 “ 

27 X 40 “ 

31 X 53 “ 

48 X 68 “ 


The usual method of fastening paper to a drawing board is by 
means of thumb tacks or small one-ounce copper or iron tacks. 
In fastening the paper by this method first fasten the upper left 
hand corner and then the lower right pulling the paper taut. The 
other two corners are then fastened, and sufficient number of tacks 
are placed along the edges to make the paper lie smoothly. For 
very fine work the paper is usually stretched and glued to the 
board. To do this the edges of the paper are first turned up all 
the way round, the margin being at least one inch. The whole 
surface of the paper included between these turned up edges is 
then moistened by means of a sponge or soft cloth and paste or 
glue is spread on the turned up edges. After removing all the 
surplus water on the paper, the edges are pressed down on the 
board, commencing at one corner. During this process of laying 
down the edges, the paper should be stretched slightly by pulling 
the edges towards the edges of the drawing board. The drawing 
board is then placed horizontally and left to dry. After the paper 
has become dry it will be found to be as smooth and tight as a 



MECHANICAL DRAWING 


5 


drum head. If, in stretching, the paper is stretched too much it 
is likely to split in drying. A slight stretch is sufficient. 

Drawing Board. The size of the drawing board depends 
upon the size of paper. Many draftsmen, however, have several 
boards of various sizes, as they are very convenient. The draw¬ 
ing board is usually made of soft pine, which should be well sea¬ 
soned and straight grained. The grain should run lengthwise of 
the board, and at the two ends there should be pieces about 1} or 
2 inches wide fastened to the board by nails or screws. These 
end pieces should be perfectly straight for accuracy in using the 
T-square. Frequently the end pieces are fastened by a glued 



kstcej ^ -— - 

DRAWING BOARD 


matched joint, nails and screws being also used. Two cleats on 
the bottom extending the whole width of the board, will reduce 
the tendency to warp, and make the board easier to move as they 
raise it from the table. 

Thumb Tacks. Thumb tacks are used for fastening the 
paper to the drawing board. They are usually made of steel 
either pressed into shape, as in the cheaper grades, or made with a 
head of German silver with the point screwed and riveted to it. 
They are made in various sizes and are very convenient as they 
can be easily removed from the board. For most work however, 








































6 


MECHANICAL DRAWING 


draftsmen use small one-ounce copper or iron tacks, as they can be 
forced flush with the drawing paper, thus offering no obstruction 
to the T-square. They also possess the advantage of cheapness. 

Pencils. In pencilling a drawing the lines should be very 
fine and light. To obtain these light lines a hard lead pencil must 
be used. Lead pencils are graded according to their hardness, 
and are numbered by using the letter H. In general a lead pencil 
of 5H (or HHHHH) or 6H should be used. A softer pencil, 4H, 
is better for making letters, figures and 
points. A hard lead pencil should be 
sharpened as shown in Fig. 1. The wood 
is cut away so that about } or \ inch 
of lead projects. The lead can then be 
sharpened to a chisel edge by rubbing it 
against a bit of sand paper or a fine file. 
It should be ground to a chisel edge and 
the corners slightly rounded. In making 
the straight lines the chisel edge should 
be used by placing it against the T-square 
or triangle, and because of the chisel edge 
the lead will remain sharp much longer than if sharpened to a point. 
This chisel edge enables the draftsman to draw a fine line exactly 
through a given point. If the drawing.is not to be inked, but is 
made for tracing or for rough usage in the shop, a softer pencil, 
3H or 4H, may be used, as the lines will then be somewhat thicker 
and heavier. The lead for compasses may also be sharpened to a 
point although some draftsmen prefer to use a chisel edge in the 
compasses as well as for the pencil. 

In using a very hard lead pencil, the chisel edge will make a 
deep depression in the paper if much pressure is put on the pencil. 
As this depression cannot be erased it is much better to press 
lightly on the pencil. 

Erasers. In making drawings, but little erasing should be 
necessary. However, in case this is necessary, a soft rubber 
should be used. In erasing a line or letter, great care must be 
exercised or the surrounding work will also become erased. To 
prevent this, some draftsmen cut a slit about 3 inches long and 
J to J inch wide in a card as shown in Fig. 2. The card is then 














MECHANICAL DRAWING 


7 


placed over the work and the line erased without erasing the rest 
of the drawing. An erasing shield of a form similar to that shown 
in Fig. 3 is very convenient, especially in erasing letters. It is 
made of thin sheet metal and is clean and durable. 

For cleaning drawings, a sponge rubber may be used. Bread 
crumbs are also used for this purpose. To clean the drawing 





r ^ 

A 




o 

o O 

1 -— 

r:.Tr:i 


0 

o O 




V 

_ J 


Fig. 2. Fig. -3. 


scatter dry bread crumbs over it and rub them on the surface 
with the hand. 

T-Square. The T-square consists of a thin straight edge 
called the blade, fastened to a head at right angles to it. It gets 



Fig. 4. 


its name from the general shape. T-squares are made of various 
materials, wood being the most commonly used. Fig. 4 shows an 
ordinary form of T-square which is adapted to most work. In 
Fig. 5 is shown a T-square with edges made of ebony or mahogany, 
as these woods are much harder than pear wood or maple, which 
is generally used. The head is formed so as to fit against the left- 
hand edge of the drawing board, while the blade extends over the 
surface. It is desirable to have the blade of the T-square form a 
right angle with the head, so that the lines drawn with the T- 
square will be at right angles to the left-hand edge of the board. 
This, however, is not absolutely necessary, because the lines drawn 
with the T-square are always with reference to one edge of the 
















8 


MECHANICAL DRAWING. 


board only, and if this edge of the board is straight, the lines 
drawn with the T-square will be parallel to each other. The T- 
square should never be used except with the left-hand edge of the 
board, as it is almost impossible to find a drawing broad with the 
edges parallel or at right angles to each other. 

The T-square with an adjustable head is frequently very con¬ 
venient, as it is sometimes necessary to draw lines parallel to each 



other which are not at right angles to the left-hand edge of the 
board. This form of T-square is similar to the ordinary T-square 
already described, but the head is swiveled so that it may be 
clamped at any desired angle. The ordinary T-square as shown 

in Figs. 4 and 5 is, how 
ever, adapted to almost 
any class of drawing. 

Fig. 6 shows the 
method of drawing parallel 
horizontal lines with the 
T-square. With the head 
of the T-square in contact 
with the left-hand edge of 
the board, the lines may be 
drawn by moving the T-square to the desired position. In using the 
T-square the upper edge should always be used for drawing as the 
two edges may not be exactly parallel and straight, and also it is 
more convenient to use this edge with the triangles. If it is neces¬ 
sary to use a straight edge for trimming drawings or cutting the 
paper from the board, the lower edge of the T-square should be 
used so that the upper edge may not be marred. 

For accurate work it is absolutely necessary that the working 
edge of the T-square should be exactly straight. To test the 























MECHANICAL DRAWING. 


9 


straightness of the edge of the T-square, two T-squares may be 
placed together as shown in Fig. 7. This figure shows plainly 
that the edge of one of the T-squares is crooked. This fact, how¬ 
ever, does not prove that either one is straight, and for this deter¬ 
mination a third blade must be r— 

used and tried with the two 
given T-squares successively. 

Triangles. 


Triangles 


are 



Fig. 7. 


made of various substances such 
as wood, rubber, celluloid and 
steel. Wooden triangles are 
cheap but are likely to warp and get out of shape. The rubber tri¬ 
angles are frequently used, and are in general satisfactory. The 
transparent celluloid triangle is, however, extensively used on ac¬ 
count of its transparency, which enables the draftsmen to see the 
work already done even when covered with the triangle. In using 
a rubber or celluloid triangle take care that it lies perfectly flat or 




is hung up when not in use ; when allowed to lie on the drawing 
board with a pencil or an eraser under one corner it will become 
warped in a short time, especially if the room is hot or the sun 
happens to strike the triangle. 

Triangles are made in various sizes, and many draftsmen 
have several constantly on hand. A triangle from 6 to 8 inches 
on a side will be found convenient for most work, although there 
are many cases where a small triangle measuring about 4 inches 














10 


MECHANICAL CHAWING. 


on a side will be found useful. Two triangles are necessary for 
every draftsman, one having two angles of 45 degrees each and 
one a right angle ; and the other having one angle of 60 degrees, 
one of 30 degrees and one of 90 degrees. 

The value of the triangle depends upon the accuracy of the 
angles and the straightness of the edges. To test the accuracy of 

the right angle of a tri¬ 
angle, place the triangle 
with the lower edge rest¬ 
ing on the edge of the 
T-square, as shown in 
Fig. 8. Now draw the 
line C D, which should be 
perpendicular to the edge 
of the T-square. The 
same triangle should then 
be placed in the position shown at B. If the right angle of the 
triangle is exactly 90 degrees the left-hand edge of the triangle 
should exactly coincide with the line C D. 

To test the accuracy of the 45-degree triangles, first test the 
right angle then place the 
triangle with the lower 
edge resting on the work¬ 
ing edge of the T-square, 
and draw the line E F as 
shown in Fig. 9. Now 
without moving the T- 
square place the triangle 
so that the other 45-degree 
angle is in the position 
occupied by the' first. If the two 45-degree angles coincide they 
are accurate. 

Triangles are very convenient in drawing lines at right 
angles to the T-square. The method of doing this is shown in 
Fig. 10. Triangles are also used in drawing lines at an angle 
with the horizontal, by placing them on the board as shown in 
Fig. 11. Suppose the line E F (Fig. 12) is drawn at any angle, 
and we wish to draw a line through the point P parallel to it. 



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o 

l\ b \ 

33 ° 1 

. 

O 

k 
































MECHANICAL DRAWING. 


If 


First place one of the triangles as shown at A, having one edge 
coinciding with the given line. Now take the other triangle and 
place one of its edges in contact Avitli the bottom edge of triangle 
A. Holding the triangle B firmly with the left hand the triangle 
A may be slipped along to the right or to the left until the edge 
of the triangle reaches the 



point P. The line M N 
may then be drawn along 
the edge of the triangle 
passing through the point 
P. In place of the tri¬ 
angle B any straight edge 
such as a T-square may be 
used. 

A line can be drawn 
perpendicular to another by means of the triangles as follows. 
Let E F (Fig. 13) be the given line, and suppose we wish to 
draw a line perpendicular to E F through the point D. Place 
the longest side of one of the triangles so that it coincides 

with the line E F, as the 



triangle is snown in posi¬ 
tion at A. Place the other 
triangle (or any straight 
edge) in the position of 
the triangle as shown at 
B, one edge resting against 
the edge of the triangle A. 
Then holding B with the 
left hand, place the tri¬ 
angle A in the position shown at C, so that the longest side 
passes through the point D. A line can then be drawn through 
the point D perpendicular to E F. 

In previous figures we have seen how lines may be drawn 
making angles of 30, 45, 60 and 00 degrees with the horizontal. 
If it is desired to draw lines forming angles of 15 and T5 degrees 
the triangles may be placed as shown in Fig. 14. 

In using the triangles and T-square almost any line may be 
drawn. Suppose we wish to draw a rectangle having one side 










































12 


MECHANICAL DRAWING. 


horizontal. First place the T-square as shown in Fig. 15. By 
moving the T-square up or down, the sides A B and D C may he 
drawn, because they are horizontal and parallel. Now place one 
of the triangles resting on the T-square as shown at E, and hav¬ 
ing the left-hand edge passing through the point D. The vertical 



line D A may be drawn, and by sliding the triangle along the edge 
of the T-square to the position F the line B C may be drawn by 
using the same edge. These positions are shown dotted in Fig. 15. 

If the rectangle is to be placed in some other position on the 
drawing board, as shown in Fig. 1G, place the 45-degree triangle 

F so that one edge is 
parallel to or coincides 
with the side I) C. Now 
holding the triangle F in 
position place the triangle 
FI so that its upper edge 
coincides with the lower 
edge, of the triangle F. 
By holding H in position 
and sliding the triangle F 
along its upper edge, the sides A B and D C may be drawn. 
To draw the sides A I) and B C the triangle should be used as 
shown at E. 

Compasses. Compasses are used for drawing circles and 
arcs of circles. They are made of various materials and in various 
sizes. The cheaper class of instruments are made of brass, but 
they are unsatisfactory on account of the odor and the tendency 
to tarnish* The best material is German silver. It does not soil 
































MECHANICAL DRAWING. 


IS 


readily, it lias no odor, and is easy to keep clean. Aluminum in¬ 
struments possess the advantage of lightness, hut on account oi 
the soft metal they do not wear well. 

The compasses are made in the form shown in Figs. 17 and 
18. Pencil and pen points are provided, as shown in Fig. 17. 
Either pen or pencil may be inserted in one leg by means of a 
shank and socket. The 
other leg is fitted with a 
needle point which is 
placed at the center of the 
circle. In most instru¬ 
ments the needle point is 
separate, and is made of a 
piece of round steel wire 
having a square shoulder 
at one or botli ends. Be¬ 
low this shoulder the needle point projects. The needle is 
made in this form so that the hole in the paper may be very 
minute. 

In some instruments lock nuts are used to hold the joint 
firmly in position. These lock nuts are thin discs of steel, witli 

notches for using a wrench or 
forked key. Fig. 19 shows the 
detail of the joint of high grade 
instruments. Both legs are alike 
at the joint, and two pivoted 
screws are inserted in the yoke. 
This permits ample movement 
of the legs, and at the same 
time gives the proper stiff¬ 
ness. The flat surface of one of 
the legs is faced with steel, the other being of German silver, 
in order that the rubbing parts may be of different metals. Small 
set screws are used to prevent the pivoted screws from turning 
in the yoke. The contact surfaces of this joint are made cir¬ 
cular to exclude dust and dirt and to prevent rusting of the 
steel face. 

Figs. 20, 21 and 22 show the detail of the socket; in some 





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L..\ \ 


--‘C 1 


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Fig. 15. 


























14 


MECHANICAL DRAWING. 


instruments the shank and socket are pentagonal, as shown in 
Fig. 20. The shank enters the socket loosely, and is held in place 
by means of the screw. Unless used very carefully this arrange¬ 
ment is not durable because the sharp corners soon wear, and the 
pressure on the set screw is not sufficient to hold the shank firmly 
in place. 

In Fig. 21 is shown another form of shank. This is round, 
haying a flat top. A set screw is also used to hold this in posi¬ 
tion. A still better form of socket is shown in Fig. 22; the hole 




Fig. 17. 



is made tapered and is circular. The shank fits accurately, and 
is held in perfect alignment by a small steel key. The clamping 
screw is placed upon the side, and keeps the two portions of the 
split socket together. 

Figs. 17 and 18 show that both legs of the compasses are 
jointed in order that the lower part of the legs may be perpen¬ 
dicular to the paper while drawing circles. In this way the 
needle point makes but a small hole in the paper, and both nibs of 
































MECHANICAL DRAWING. 


15 


the pen will press equally oil the paper. In pencilling circles it 
is not as necessary that the pencil should be kept vertical; it is a 
good plan, however, to learn to use them in this way both in pen¬ 
cilling and inking. The com¬ 
passes should be held loosely be¬ 
tween the thumb and forefinger. 

If the needle point is sharp, as 
it should be, only a slight pres¬ 
sure will be required to keep it 
in place. While drawing the 
circle, incline the compasses 
slightly in the direction of 
revolution and press lightly on 
the pencil or pen. 

In removing the pencil or 
pen, it should be pulled out Fi g- 

straight. If bent from side to side the socket will become en¬ 
larged and the shank worn; this will render the instrument inac¬ 
curate. For drawing large circles the lengthening bar shown in 
Fig. IT should be used. When using the lengthening bar the 







Fig. 20- 


Fig. 21. 


needle point should be steadied with, one hand and the circle 
described with the other. 

Dividers. Dividers, shown in Fig. 23, are made similar to the 
compasses. They are used for laying off distances on the draw¬ 
ing, either from scales or from other parts of the drawing. They 

may also be used for dividing a line 
ijrl into equal parts. When dividing a 
line into equal parts the dividers 
should be turned in the opposite direc¬ 
tion each time, so that the moving point passes alternately to 
the right and to the left. The instrument can then be operated 
readily with one hand. The points of the dividers should be 
very sharp so that the holes made in the paper will be small. 
If large holes are made in the paper, and the distances between 


B 


Fig. 22. 






























16 


MECHANICAL DRAWING. 


the points are not exact, accurate spacing cannot be done 
Sometimes the compasses are furnished with steel divider points 
in addition to the pen and pencil points. The compasses may 
then be used either as dividers or as compasses. Many drafts¬ 
men use a needle 'point in place of dividers for making measure¬ 
ments from a scale. The eye end of a needle is first broken off 
and the needle then forced into a small handle made of a round 
piece of soft pine. This instrument is very convenient 
for indicating the intersection of lines and marking off 
distances. 

Bow Pen and Bow Pencil. Ordinary large compasses 
are too heavy to use in making small circles, fillets, etc. 
The leverage of the long leg is so great that it is very 
difficult to draw small circles accurately. For this reason 
the bow compasses shown in Figs. 24 and 25 should be 
used on all arcs and circles having a radius of less than 
three-quarters inch. The bow compasses are also con¬ 
venient for duplicating small circles such as those which 
represent boiler tubes, bolt holes,.etc., «ince there is no 
tendency to slip. 

The needle point must be adjusted to the same 
length as the pen or pencil point if very small circles are 
to be drawn. The adjustment for altering the radius of 
the circle can be made by turning the nut. If the change 
in radius is considerable the points should be pressed to¬ 
gether to remove the pressure from the nut which can 
then be turned in either direction with but little wear on 
the threads. 

Fig. 26 shows another bow instrument which is frequently 
used in small work in place of the dividers. It has the advantage 
of retaining the adjustment. 

Drawing Pen. For drawing straight lines and curves that 
are not arcs of circles, the line pen (sometimes called the ruling 
pen) is used. It consists of two blades of steel fastened to a 
handle as shown in Fig. 27. The distance between the pen points 
can be adjusted by the thumb screw, thus regulating the width of 
Line to be drawn. Tlie blades are given a slight curvature so that 
there will be a cavity for ink when the points are close together. 


J 


Fig. 23. 











MECHANICAL DRAWING. 


17 


The pen may be filled by means of a common steel pen or 
with the quill which is provided with some liquid inks. The pen 
should not be dipped in the ink because it will then be necessary 
to wipe the outside of the blades before use. The ink should 
fill the pen to a height of about \ or inch; if too much ink is 
placed in the pen it is likely to drop out and spoil the drawing. 
Upon finishing the work the pen should be carefully wiped with 


h 

Fig. 26. 

chamois or a soft cloth, because most liquid inks corrode the steel. 

In using the pen, care should be taken that both blades bear 
equally on the paper. If the points do not bear equally the line 
will be ragged. If both points touch, and the pen is in good 
condition the line will be smooth. The pen is usually inclined 
slightly in the direction in which the line is drawn. The pen 



Fig. 27. 


should touch the triangle or T-square which serve as guides, but 
it should not be pressed against them because the lines will then 
be uneven. The points of the pen should be close to the edge of 
the triangle or T-square, but should not touch it. 

To Sharpen the Drawing Pen. After the pen has been 
used for some time the points become worn, and it is impossible 



Fig. 24. Fig. 25. 













18 


MECHANICAL DRAWING. 


to make smooth lines. This is especially true if rough paper is 
used. The pen can be put in proper condition by sharpening it. 
To do this take a small, flat, close-grained oil-stone. The blades 
should first be screwed together, and the points of the pen can be 
given the proper shape by drawing the pen back and forth over 
the stone changing the inclination so that the shape of the ends 
will be parabolic. This process dulls the points but gives them 
the proper shape, and makes them of the same length. 

To sharpen the pen, separate the points slightly and rub one 
of them on the oil-stone. While doing this keep the pen at an 
angle of from 10 to 15 degrees with the face of the stone, and 
give it a slight twisting movement. This part of the operation 
requires great care as the shape of the. ends must not be altered. 
After the pen point has become fairly sharp the other point 
should be ground in the same manner. All the grinding should 
be done on the outside of the blades. The burr should be 
removed from the inside of the blades by using a piece of leather 
or a piece of pine wood. 

Ink should now be placed between the blades and the pen 
tried. The pen should make a smooth line whether fine or 
heavy, but if it does not the grinding must be continued and the 
pen tried frequently. 

Ink. India ink is always used for drawing as it makes a 
permanent black line. It maybe purchased in solid stick form 
or as a liquid. The liquid form is very convenient as much time 
is saved, and all the lines will be of the same color; the acid in 
the ink, however, corrodes steel and makes it necessary to keep 
the pen perfectly clean. 

Some draftsmen prefer to use the India ink which comes in 
stick form. To prepare it for use, a little water should be placed 
in a saucer and one end of the stick placed in it. The ink is 
ground by giving it a twisting movement. When the water has 
become black and slightly thickened, it should be tried. A 
heavy line should be made on a sheet of paper and allowed to 
dry. If the line has a grayish appearance, more grinding is 
necessary. After the ink is thick enough to make a good black 
line, the grinding should cease, because very thick ink will not 
flow freely from the pen. If, however, the ink lias become too 



MECHANICAL DRAWING. 




thick, it may be diluted with water. After using, the stick 
should be wiped dry to prevent crumbling. It is well to grind 
the ink in small quantities as it does not dissolve readily if it has 
once become dry. If the ink is kept covered it will keep for two 
or three days. 

Scales. Scales are used for obtaining the various measure¬ 
ments on drawings. They are made in several forms, the most 
convenient being the flat with beveled edges and the triangular. 
The scale is usually a little over 12 inches long and is graduated 
for a distance of 12 inches. The triangular scale shown in Fig. 
28 has six surfaces for graduations, thus allowing many gradua¬ 
tions on the same scare. 

The graduations on the scales are arranged so that the 
drawings may be made in any proportion to the actual size. For 
mechanical woyk, the common divisions are multiples of two. 



Fig. 28. 


Thus we make drawings full size, half size, Jg, J 2 , g^, etc. 
i f a drawing is ^ size, 8 inches equals 1 foot, hence 8 inches is 
divided into 12 equal parts and each division represents one inch. 
If the smallest division on a scale represents Jg inch, the scale is 
said to read to -Jg- inch. 

Scales are often divided into y 1 ^, 2 V Fo’ A’ e ^ c *’ ^ or arc ^i- 
tects, civil engineers, and for measuring on indicator cards. 

The scale should never be used for drawing lines in place of 
triangles or T-square. 

Protractor. The protractor is an instrument used for laying 
off and measuring angles. It is made of steel, brass, horn and 
paper. If made of metal the central portion is cut out as shown 
in Fig. 29, so that the draftsman can see the drawing. The 
outer edge is divided into degrees and tenths of degrees. Some¬ 
times the graduations are very fine. In using a protractor a very 
sharp hard pencil should be used so that the lines will be fine 
and accurate. 

The protractor should be placed so that the given line ( pro- 








2U 


MECHANICAL DRAWING. 


duced if necessary) coincides with the two O marks. The 
center of the circle being placed at the point through which the 
desired line is to be drawn. The division can then be marked 
with the pencil point or needle point. 

Irregular Curve, One of the conveniences of a draftsman’s 



outfit is the French or irregular curve. It is made of wood, 
hard rubber or celluloid, the last named material being the best. 
It is made in various shapes, two of the most common being 



shown m Fig. 30. This instrument is used for drawing curves 
other than arcs of circles, and both pencil and line pen can be 
used. 

To draw the curve, a series of points is first located and 
then the curve drawn passing through them by using the part of 
the irregular curve that passes through several of them. The 









MECHANICAL DRAWING. 


‘ 1 L 


curve is shifted for this work from one position to another. It 
frequently facilitates the work and improves its appearance to 
draw a free hand pencil curve through the points and then use the 
irregular curve, taking care that it always fits at least three points. 

In inking the curve, the blades of the pen must be kept 



Fig. 31. 



tangent to the curve, thus necessitating a continual change of 
direction. 

Beam Compasses. The ordinary compasses are not large 
enough to draw circles having a diameter greater than •about 8 or 
10 inches. A convenient instrument for larger circles is found 
in the beam compasses shown in Fig. 31. The two parts called 
channels carrying the pen or pencil and the needle point are 
clamped to a wooden beam ; the distance between them being 
equal to the radius of the circle. Accurate adjustment is obtained 
by means of a thumb nut underneath one of the channel pieces. 


LETTERING. 

No mechanical drawing is finished unless all headings, titles 
and dimensions are lettered in plain, neat type. Many drawings 
are accurate, well-planned and finely executed but do not present 
a good appearance because the draftsman did not think it worth 
while to letter well. Lettering requires time and patience; 
and if one wishes to letter rapidly and well he must practice. 

Usually a beginner cannot letter well, and in order to pro 
duce a satisfactory result, considerable practice is necessary. Many 
























2‘4 


MECHANICAL DRAWING. 


think it a good plan to practice lettering before commencing a 
drawing. A good writer does not always letter well; a poor 
writer need not be discouraged and think he can never learn to 
make a neatly lettered drawing. 

In making large letters for titles and headings it is often 
necessary to use drawing instruments and mechanical aids. The 
small letters, such as those used for dimensions, names of materials, 
dates, etc., should be made free hand. 

There are many styles of letters used by draftsmen. For 
titles, large Roman capitals are frequently used, although Gothic 
and block letters also look well and are much easier to make. 

ABCDE FGHIJ 
KLMNOPQR 
STUVWXYZ 
1234567890 

Fig. 32. 

Almost any neat letter free from ornamentation is acceptable in the 
regular practice of drafting. Fig. 32 shows the alphabet ot 
vertical Gothic capitals. These letters are neat, plain and easily 
made. The inclined or italicized Gothic type is shown in Fig. 33. 
This style is also easy to construct, and possesses the advantage 
that a slight difference in inclination is not apparent. If the ver¬ 
tical lines of the vertical letters incline slightly the inaccuracy is 
very noticeable. 

The curves of the inclined Gothic letters such as those in the 
B , 6 V , Cr, etc., are somewhat difficult to make free hand, 
especially if the letters are about one-half inch high. In the 
alphabet shown in Fig. 34, the letters are made almost wholly of 



MECHANICAL DRAWING. 


23 


straight lines, the corners only being curved. These letters are 
very easy to make and are clear cut. 

The first few plates of this work will require no titles; the 
only lettering being the student’s name, together with the date 
and plate number. Later, the student will take up the subject of 

ABCDETGH/J 
KL MNOBQB 
STUVWXYZ 

Fig. 33. 

lettering again in order to letter titles and headings for drawings 
showing the details of machines. For the present, however, in¬ 
clined Gothic capitals will be used. 

To make the inclined Gothic letters, first draw two parallel 
lines having the distance between them equal to the desired height 
of the letters. If two sizes of letters are to be used, the smaller 
should be about two-thirds as high as the larger. For the letters 

^ 1 BODEPGHUKLM 
NOP OR S TU VWX YZ 
/B3X567830 

Fig. 34. 

to be used on the first plates, draw two parallel lines inch apart. 
This is the height for the letters of the date, name, also the plate 
number, and should be used on all plates throughout this work, 
unless other directions are given. 

In constructing the letters, they should extend fully to these 
lines, both at the top and bottom. They should not fall short of 



24 


MECHANICAL DRAWING. 


the guide lines nor extend beyond them. As these letters are 
inclined they will look better if the inclination is the same for all. 
As an aid to the beginner, he can draw light pencil lines, about } 
inch apart, forming the proper angle with the parallel lines already 
drawn. The inclination is often made about 70 degrees; but as a 
60-degree triangle is at hand, it may be used. To draw these 
lines place the 60-degree triangle on the T-square as shown in 
Fig. 86. In making these letters the 60-degree lines will be 
found a great aid as a large proportion of the back or side lines 
have this inclination. 

Capital letters such as P,’ F, P, P, Z, etc., should have the 
top lines coincide with the upper horizontal guide line. The 
bottom lines of such letters as D, P, P, Z , etc., should coincide 
with the lower horizontal guide line. If these lines do not coin¬ 
cide with the guide lines the words will look uneven. Letters, 
of which(7, 6r, 0, and Q , are t}^pes, can be formed of curved lines 
or of straight lines. If made of curved lines, they should have a 
little greater height than the guide lines to prevent their appear¬ 
ing smaller than the other letters. In this work they can be 
made of straight lines with rounded corners as they are easily 
constructed and the student can make all letters of the same 
height. 

To construct the letter A, draw a line at an angle of 60 
degrees to the horizontal and use it as a center line. Then from 
the intersection of this line and the upper horizontal line drop 
a vertical line to the lower guide line. Draw another line from 
the vertex meeting the lower guide line at the same distance from 
the center line. The cross line of the A should be a little below 
the center. The Pis an inverted A without the cross line. For 
the letter AT, the side lines should be parallel and about the same 
distance apart as are the horizontal lines. The side lines of the 
W are not parallel but are farther apart at the top. The J is not 
quite as wide as such letters as P", P, P, P, etc. To make a Y. 
draw the center line 60 degrees to the horizontal; the diverg¬ 
ing lines are similar to those of the V but are shorter and form a 
larger angle. The diverging lines should meet the center line a 
little below the middle. 

The lower-case letters are shown in Fig. 85. In such letters 



MECHANICAL DRAWING. 


25 


as m, n , r, etc., make the corners sharp and not rounding. The 
letters a, b, c, g, 0, j?, q, should be full and rounding. The 
figures (see Fig. 32) are made as in writing — except the 0,8 
and 9 . 

The Roman numerals are made of straight lines as they 
are largely made up of I, V and X. 

At first the copy should be followed closely and the letters 
irawn in pencil. For a time, the inclined guide lines may be used, 

abcc/efgh/jk/mn 
opqrrs tuvwxj'z 

F5£. 35. 

but after the proper inclination becomes firmly fixed in mind 
they should be abandoned. The horizontal lines are used at all 
times by most draftsmen. After the student has had consider¬ 
able practice, he can construct the letters in ink without first using 
the pencil. Later in the work, when the student has become pro¬ 
ficient in the simple inclined Gothic capitals, the vertical, block 
and Roman alphabets should be studied. 

PLATES, 

To lay out a sheet of paper for the plates of this work, the 
sheet, A B G F, (Fig. 36) is placed on the drawing board 2 or 3 
inches from the left-hand edge which is called the working edge . 
If placed near the left-hand edge, the T-square and triangles can 
be used with greater firmness and the horizontal lines drawn with 
the T-square will be more accurate. In placing the paper on the 
board, always true it up according to the long edge of the sheet. 
First fasten the paper to the board with thumb tacks, using at 
least 4 — one at each corner. If the paper has a tendency to curl 
it is better to use 6 or 8 tacks, placing them as shown in Fig. 36. 
Thumb tacks are commonly used; but many draftsmen prefer 
one-ounce tacks as they offer less obstruction to the T-square and 
triangles. 

After the paper is fastened in position, find the center of the 



26 


MECHANICAL DRAWING?. 








































MECHANICAL DRAWING. 


27 


sheet by placing the T-square so that its upper edge coincides with 
the diagonal corners A and G and then with the corners F and 
B, drawing short pencil lines intersecting at C. Now place the 
T-square so that its upper edge coincides with the point C and 
draw the dot and dash line D E. With the T-square and one 
of the triangles (shown dotted) in the position shown in Fig. 36, 
draw the dot and dash line HCK. In case the drawing board 
is large enough, the line C H can be drawn by moving the T- 
square until it is entirely off the drawing. If the board is small, 
produce (extend) the line K C to H by means of the T-square 
or edge of a triangle. In this work always move the pencil from 
the left to the right or from the bottom upward; never (except 
for some particular purpose) in the opposite direction. 

After the center lines are drawn measure off 5 inches above 
and below the point C on the line H 0 K. These points L 
and M may be indicated by a light pencil mark or by a slight 
puncture of one of the points of the dividers. Now place the T- 
square against the left-hand edge of the board and draw horizontal 
pencil lines through L and M. 

Measure off 7 inches to the left and right of C on the center 
line D C E and draw pencil lines through these points (N and 
P) perpendicular to D E. We now have a rectangle 10 inches 
by 14 inches, in which all the exercises and figures are to be 
drawn. The lettering of the student’s name and address, date, 
and plate number are to be placed outside of this rectangle in the 
i-inch margin. In all cases lay out the plates in this manner and 
keep the center lines D E and K H as a basis for the various 
figures. The border line is to be inked with a heavy line when 
the drawing is inked. 

Pencilling. In laying out plates, all work is first done in pen¬ 
cil and afterward inked or traced on tracing cloth. The first few 
plates of this course are to be done in pencil and then inked ; later 
the subject of tracing and the process of making blue prints will 
be taken up. Every beginner should practice with his instruments 
qntil he can use them with accuracy and skill, and until he under¬ 
stands thoroughly what instrument should be used for making a 
given line. To aid the beginner in this work, the first three plates 
of this course are designed to give the student practice; they do 



ilECIIAXICAT, DRAWING. 


as 


not involve any problems and none of the work is difficult. The 
student is strongly advised to draw these plates two or three 
times before making the one to be sent to us for correction. Dili¬ 
gent practice is necessary at first; especially on PLATE /as it 
involves an exercise in lettering. 

PLATE I. 

Pencilling-. To draw PLATE 1 ’ take a sheet of drawing 
paper at least 11 inches by 15 inches and fasten it to the drawing 
board as already explained. Find the center of the sheet and draw 
fine pencil lines to’represent the lines D E and H K of Fig. 36. 
Also draw the border lines L, M, N and P. 

Now measure |- inch above and below the horizontal center line 
and, Avith the T-square, draw lines through these points. These 
lines will form the lower lines D C of Figs. 1 and 2 and the top lines 
A B of Figs. 3 and Jf. Measure | inch to the right and left of the 
vertical center line; and through these points, draw lines parallel 
to the center line. These lines should be drawn by placing the 
triangle on the T-square as shown in Fig. 36. The lines thus 
drawn, form the sides B C of Figs. 1 and 3 and the sides A D of 
Figs. 2 and Jj,. Next draw the line A B A B with the T-square, 
4| inches above the horizontal center line. This line forms the 
top lines of Figs. 1 and 2. Now draw the line D C D C 4| inches 
below the horizontal center line. The rectangles of the four 
figures are completed by drawing vertical lines 6| inches from the 
vertical center line. We now have four rectangles each 6J inches 
long and 4-^ inches wide. 

Fig. 1 is an exercise with the line pen and T-square. Divide 
the line A D into divisions each ^ inch long, making a fine pencil 
point or slight puncture at each division such as E, F, G, H, I, etc. 
Now place the T-square with the head at the left-hand edge of the 
drawing board and through these points draw light pencil lines 
extending to the line B C. In drawing these lines be careful to 
have the pencil point pass exactly through the division marks so 
that the lines will be the same distance apart. Start each line in 
the line A D and do not fall short of the line B C or run over it. 
Accuracy and neatness in pencilling insure an accurate drawing. 
Some beginners think that they can correct inaccuracies while 



























































































* 
































































PLATE I 





JANUARY /. /90 7 j HERBERT CHANDLER CH/CAGD, /LL. 





















































































MECHANICAL DRAWING. 


29 


inking; but experience soon teaches them that they cannot do so. 

Fig . 2 is an exercise with the line pen, T-square and triangle. 
First divide the lower line D C of the rectangle into divisions each 
| inch long and mark the points E, F, G, H, I, J, K, etc., as in 
Fig. 1. Place the T-square with the head at the left-hand edge of 
the drawing board and the upper edge in about the position shown 
in Fig. 36. Place either triangle with one edge on the upper edge 
of the T-square and the 90-degree angle at the left. Now draw 
fine pencil lines from the line D C to the line A B passing through 
the points E, F, G, H, I, J, K, etc. To do this keep the T-square 


Y 

E 

T 

- / f- / /A 

- R/NG 



/ Mh F///H, / 




/ 




A A//GA7 




/^>r/-r7i7 




D/SF/G " 





/-^ror 7 aen 





oy Jjf a oltoh 


J r 


AHt :/ )F 





TTOTTZm 








7 77 7T7 7V 


Z 

X 


Fig. 37. 


rigid and slide the triangle toward the right, being careful to have 
the edge coincide with the division marks in succession. 

Fig. 3 is an exercise with the line pen, T-square and 45-degree 
triangle. First lay off the distances A E, E F,FG, GH,HI,IJ, 
J K, etc., each \ inch long. Then lay off the distances B L, L M, 
M N, N O, O P, P Q, Q R, etc., also \ inch long. Place the T- 
square so that the upper edge will be below the line D C of Fig . 3 . 
With the 45-degree triangle draw lines from A D and D C to 
the points E, F, G, H, I, J, K, etc., as far as the point B. Now 
draw lines from D C to the points L, M, N, O, P, Q, R, etc., as 





































so 


MECHANICAL DRAWING. 


far as the point C. In drawing these lines move the pencil away 
from the tody, that is, from A D to A B and from D C to B C. 

Fig. is an exercise in free-hand lettering. The finished 
exercise, with all guide lines Erased, should have the appearance 
shown in Fig . £ of PLATE I. The guide lines are drawn as shown 
in Fig, 3T. First draw the center line E F and light pencil lines 
Y Z and 1 X, | inch from the border lines. Now, with the T- 
square, draw the line G, | inch from the top line and the line H, 
jgp 2 inch below G. The word “ LETTERING- ” is to be placed 
between these two lines. Draw the line I, ^ inch below H. 
The lines I, J, etc., to K are all ^ inch apart. 

We npw practice the lower-case letters. Draw the line L, T S g 
inch below K and a light line A inch above L to limit the 
height of the small letters. The space between L and M is ^ 
inch. The lines M and N are drawn in the same manner as K and 
L. The space between N and O should be 1 inch. The line P is 
drawn inch below (X Q is also ^ inch below P. The lines 
Q and R are drawn ^ inch apart as are M and N. The remainder 
of the lines S, U, Y and W are drawn ^ inch apart. 

The center line is a great aid in centering the word 
“ LETTERING” the alphabets, numerals, etc. The words 
“THE ” and “ Proficiency ” should be indented about J- 
inch as they are the first words of paragraphs. To draw the 
guide lines, mark off distances of ^ inch on any line such as J and 
with the 60-degree triangle draw light pencil lines cutting the 
parallel lines. The letters should be sketched in pencil, the ordin¬ 
ary letters such as E, F, II, N, R, etc. being made of a width 
equal to about | the height. Letters like A, M and W are wider. 
The space between the letters depends upon the draftsman’s 
taste but the beginner should remember that letters next to an 
A or an L should be placed near them and that greater space 
should be left on each side of an I or between letters whose sides are 
parallel; for instance there should be more space between an N and 
E than between an E and H. On account of the space above the 
lower line of the L, a letter following an L should be close to it 
If a T follows a T or the letter L follows an L they should be 
placed near together. In all lettering the letters should be placed 
so that the general effect is pleasing. After the four figures are 



MECHANICAL DRAWING. 


31 


completed, the lettering for name, address and date should be 
pencilled. With the T-square draw a pencil line -fa inch above 
the top border line at the right-hand end. This line should be 
about 3 inches long. At a distance of inch above this line draw 
another line of about the same length. These are the guide lines 
for the word PLATE I. The letters should be pencilled free 
hand and the student may use the 60-degree guide lines if he 
desires. 

The guide lines of the date, name and address are similarly 
drawn in the lower margin. The date of completing the drawing 
should be placed under Fig. 3 and the name and address at the 
right under Fig. The street address is unnecessary. It is a 
good plan to draw lines ^ i nc h a P ar ^ on a separate sheet of paper 
and pencil the letters in order to know just how much space each 
word will require. The insertion of the words “ Fig. 1” “ Fig. 
2” etc., is optional with the student. He may leave them out if he 
desires ; but we would advise him to do this extra lettering for the 
practice and for convenience in reference. First draw with the 
T-square two parallel line inch apart under each exercise; the 
lower line being Jg inch above the horizontal center line or above 
the lower border line. 

Inking. After all of the pencilling of PLATE I has been 
completed the exercises should be inked. The pen should first be 
examined to make Sure that the nibs are clean, of the same length 
and come together evenly. To fill the pen with ink use an ordi¬ 
nary steel pen or the quill in the bottle, if Higgin’s Ink is used. 
Dip the quill or pen into the bottle and then inside between the 
nibs of the line pen. The ink will readily flow from the quill into 
the space between the nibs as soon as it is brought in contact. Do 
not fill the pen too full, if the ink fills about \ the distance to the 
adjusting screw it usually will be sufficient. If the filling has been 
carefully done it will not be necessary to wipe the outsides of the 
blades. However, any ink on the outside should be wiped off 
with a soft cloth or a piece of chamois. 

The pen should now be tried on a separate piece of paper in 
order that the width of the line may be adjusted. In the first 
work where no shading is done, a firm distinct line should be used. 
The beginner should avoid the extremes; a very light line makes 



32 


MECHANICAL DRAWING. 


the drawing have a weak, indistinct appearance, and very heavy 
lines detract from the artistic appearance and make the drawing 
appear heavy. 

Til case the ink does not flow freely, wet the finger and touch 
it to the end of the pen. If it then fails to flow, draw a slip of 
thin paper between the nibs (thus removing the dried ink) or 
clean thoroughly and fill. Never lay the pen aside without 
cleaning. 

In ruling with the line pen it should be held firmly in the 
right hand almost perpendicular to the paper. If grasped too 
firmly the width of the line may be varied and the draftsman 
soon becomes fatigued. The pen is usually held so that the 
adjusting screw is away from the T-square, triangles, etc. Many 
draftsmen incline the pen slightly in the direction in which it is 
moving. 

To ink Fig. 1 , place the T-square with the head at the work¬ 
ing edge as in pencilling. First ink all of the horizontal lines 
moving the T-square from A to D. In drawing these lines con¬ 
siderable care is necessary; both nibs should touch the paper and 
the pressure should be uniform. Have sufficient ink in the pen 
to finish the line as it is difficult for a beginner to stop in the 
middle of the line and after refilling the pen make a smooth con¬ 
tinuous line. While inking the lines A, E, F, G, H, I, etc., greater 
care should be taken in starting and stopping than while pencil¬ 
ling. Each line should start exactly in the pencil line A D and 
stop in the line B C. The lines A D and B C are inked, using 
the triangle and T-square. 

Fig . 2 is inked in the same manner as it was pencilled; the 
lines being drawn, sliding the triangle along the T-square in the 
successive positions. 

In inking Fig. 5, the same care is necessary as with the pre¬ 
ceding, and after the oblique lines are inked the border lines are 
finished. In Fig. ^ the border lines should be inked in first 
and then the border lines of the plate. The border lines should 
be quite heavy as they give the plate a better appearance. The 
intersections should be accurate, as any running over necessitates 
erasing. 

The line pen may now be cleaned and laid aside. It can be 





















































































. 





















PLATE _ZT 





















































































































































































































































































MECHANICAL DRAWING. 


33 


cleaned by drawing a strip of blotting paper between the nibs or 
by means of a piece of cloth or chamois. The lettering should be 
done free-hand using a steel pen. If the pen is very fine, accu¬ 
rate work may be done but the pen is likely to catch in the paper, 
especially if the paper is rough. A coarser pen will make broader 
lines but is on the whole preferable. Gillott’s 404 is as fine a 
pen as should be used. After inking Fig. the plate number, 
date and name should be inked, also free-hand. After ink¬ 
ing the words “ Fig . _Z,” “ Fig. 2” etc., all pencil lines should 
be erased. In the finished drawing there should be no center 
lines, construction lines or letters other than those in the 
name, date, etc. 

The sheet should be cut to a size of ii inches by 15 inches, 

the dash line outside the border line of PLATE /indicating the 
edge. 

PLATE II. 

Pencilling. The drawing paper used for PLATE II should 
be laid out as described with PLATE I, that is, the border lines, 
center line and rectangles for Figs. 1 and 2. To lay out Figs. 3, 
^ and 5 proceed as follows : Draw a line with the T-square 
parallel to the horizontal center line and | inch below it. Also 
draw another similar line 4| below the center line. The two lines 
will form the top and bottom of Figs. 3 , £ and Now measure 
off 2^ inches on either side of the center on the horizontal center 
line and call the points Y and Z. On either side of Y and Z and 
at a distance of ^ inch draw vertical parallel lines. Now draw a 
vertical line A D, 4^ inches from the line Y and a vertical line 
B C 4| inches from the line Z. We now have three rectangles 
each 4 inches broad and 4| inches high. Figs. 1 and 2 are pen¬ 
cilled in exactly the same way as was Fig. 1 of PLATE /, that 
is, horizontal lines are drawn ^ inch apart. 

Fig. 3 is an exercise to show the use of a 60-degree triangle 
with a T-square. Lay off the distances A E, E F, F G, G H, etc. 
to B each \ inch. With the 60 degree triangle resting on the 
upper edge of the T-square, draw lines through these points, E, F, 
G, H, I, J, etc., forming an angle of 30 degrees with the hori¬ 
zontal. The last line drawn will be A L. In drawing these lines 
move the pencil from A B to B C. Now find the distance 



34 


MECHANICAL DRAWING. 


between the lines on the vertical B L and mark off these distances 
on the line B C commencing at L. Continue the lines from A L 
to N C. Commencing at N mark off distances on A D equal 
to those on B C and finish drawing the oblique lines. 

Fig. £ is exercise for intersection. Lay off distances of 
^ inch on A B and AD. With the T-square draw fine pencil 
lines through the points E, F, G, H, I, etc., and with the T-square 
and triangle draw vertical lines through the points L, M, N, O, P, 
etc. In drawing this figure draw every line exactly through the 
points indicated as the symmetrical appearance of the small 
squares can be attained only by accurate pencilling. 

The oblique lines in Fig. 5 form an angle of 60 degrees with 
the horizontal. As in Figs. 3 and ^ mark off the line A B in 
divisions of J inch and draw with the T-square and 60-degree 
triangle the oblique lines through these points of division moving 
the pencil from A B to B C. The last line thus drawn will be 
A L. Now mark off distances of ^ inch on C D beginning at L. 
The lines may now be finished. 

Inking. Fig. 1 is designed to give the beginner practice in 
drawing lines of varying widths. The line E is first drawn. This 
line should be rather fine but should be clear and distinct. The 
line F should be a little wider than E; the greater width being 
obtained by turning the adjusting screw from one-quarter to one- 
half a turn. The lines G, H, I, etc., are drawn; each successive 
line having greater width. M and N should be the same and 
quite heavy. From N to D the lines should decrease in width. 
To complete the inking of Fig. 1, draw the border lines. These 
lines should have about the same width as those in PLATE I. 

In Fig. 2 the first four lines should be dotted. The dots should 
be uniform in length (about -fa inch) and the spaces also uniform 
(about 3 V inch). The next four lines are dash lines similar to 
those used for dimensions. These lines should be drawn with 
dashes about | inch long and the lines should be fine, yet distinct. 

The following four lines are called dot and dash lines. The 
dashes are about | inch long and a dot between as shown. In 
the regular practice of drafting the length of the dashes depends 
upon the size of the drawing — 4. inch to ,1 inch being common. 
The last four lines are similar, two dots being used between the 



mechanical drawing. 


36 


dashes. After completing the dot and dash lines, draw the border 
lines of the rectangle as before. 

In inking Fig. 3, the pencil lines are followed. Great care 
should be exercised in starting and stopping. The lines should 
begin in the border lines and the end should not run over. 

The lines of Fig. If must be drawn carefully, as there are so 
many intersections. The lines in this figure should be lighter than 
the border lines. If every line does not coincide with the points 
of division L, M, N, O, P, etc., some will appear farther apart 
than others. 

Fig. 5 is similar to Fig. 3, the only difference being in the 
angle which the oblique lines make with the horizontal. 

After completing the five figures draw the border lines of the 
plate and then letter the plate number, date and name, and the 
figure numbers, as in PLATE I. The plate should then be 
cut to the required size, n inches by 15 inches. 

PLATE III. 

Pencilling. The horizontal and vertical center lines and the 
border lines for PLATE III are laid out in the same manner as 
were those of PLATE II. To draw the squares for the six figures, 
proceed as follows: 

Measure off two inches on either side of the vertical center 
line and draw light pencil lines through these points parallel to 
the vertical center line. These lines will form the sides A D and 
B C of Figs. 2 and 5. Parallel to these lines and at a distance of 
| inch draw similar lines to form the sides B C of Figs. 1 and If 
and A D of Figs. 3 and 6. The vertical sides A D of Figs. 1 and 
If and B C of Figs. 3 and 6 are formed by drawing lines perpen¬ 
dicular to the horizontal center line at a distance of 6^ inches from 
the center. 

The horizontal sides D C of Figs. 1 , 2 and 3 are drawn with 
the T-square i inch above the horizontal center line. To draw the 
top lines of these figures, draw (with the T-square) a line 4J inches 
above the horizontal center line. The top lines of Figs . If, 5 and 
6 are drawn \ inch below the horizontal center line. The squares 
are completed by drawing the lower lines D C, 4| inches below 
the horizontal center line. The figures of PLATES I and 11 



MECHANICAL DRAWING. 


36 


were constructed in rectangles; the exercises of PLATE III are, 
however, drawn in squares, having the sides 4 inches long. 

In drawing Fig. 1, first divide A D and A B (or DC) into 
4 equal parts. As these lines are four inches long, each length will 
be 1 inch. Now draw horizontal lines through E, F and G and 
vertical lines through L, M and N. These lines are shown dotted 
in Fig. 1. Connect A and B with the intersection of lines E 
and M, and A and D with the intersection of lines F and L. 
Similarly draw D J, J C, I B and I C. Also connect the points P, 
O, I and J forming a square. The four diamond shaped areas 
are formed by drawing lines from the middle points of A D, A B, 
B C and DC to the middle points of lines A P, A O, O B, I B 
etc., as shown in Fig. 1. 

Fig . 2 is an exercise of straight lines. Divide A D and A B 
Into four equal parts and draw horizontal and vertical lines as in 
Fig . 1. Now divide these dimensions, A L, M N, etc. and E F, 
G B etc. into four equal parts (each ^ inch ). Draw light 
pencil lines with the T-square and triangle as shown in Fig. 2. 

In Fig. 3 , divide A B and A D into eight parts, each length 
being J inch. Through the points H, I, J, K, L, M and N draw 
vertical lines with the triangle. Through O, P, Q, R, S, T and U 
draw horizontal lines with the T-square. Now draw lines con¬ 
necting O and H, P and I, Q and J, etc. These lines can be 
drawn with the 45-degree triangle, as they form an angle of 45 
degrees with the horizontal. Starting at N draw lines from A B 
to B C at an angle of 45 degrees. Also draw lines from A D to 
D C through the points O, P, Q, R, etc., forming angles of 45 
degrees with D C. 

Fig . 4 is drawn with the compasses. First draw the diagonals 
A C and D B. With the T-square draw the line E H. Now 
mark off on E H distances of \ inch. With the compasses set so 
that the point of the lead is 2 inches from the needle point, de¬ 
scribe the circle passing through E. With H as a center draw 
the arcs F G and I J having a radius of 1J inches. In drawing 
these arcs be careful not to go beyond the diagonals, but stop at 
the points F and G and I and J. Again with H as the center 
and a radius of 1| inches draw a circle. The arcs K L and M N 
are drawn in the same manner as were arcs F G and I J; tha 




PLATE HL 



•JANUARY* /A, /9Q7 HERBERT CHANJOLEH CH/OAOO, /LL. 


















































































































































































MECHANICAL DRAWING. 


37 


radius being 1^ inches. Now draw circles, with H as the center, 
of 1, | and 1 inch radius, passing through the points P, T, etc. 

Fig. 5 is an exercise with the line pen and compasses. First 
draw the diagonals A C and D B, the horizontal line L M and the 
vertical line E F passing through the center Q. Mark off dis¬ 
tances of | inch on L M and E F and draw the lines N N' O O' 
and N R, O S, etc., through these points, forming the squares 
N R R' N0 S S' O', etc. With the bow pencil adjusted so 
that the distance between the pencil point and the needle point is 
inch draw the arcs having centers at the corners of the squares. 
The arc whose center is N will be tangent to the lines A L and 
A E and the arc whose center is O will be tangent to N N' and 
N R. Since P T, T T', T' P' and P' P are each 1 inch long and 
form the square, the arcs drawn with Q as a center will form a 
circle. 

To draw Fig. 6 , first draw the center lines E F and L M. 
Now find the centers of the small squares A L I E, L B F I etc. 
Through the center I draw the construction lines HIT and 
RIP forming angles of 80 degrees with the horizontal. Now 
adjust the compasses to draw circles having a radius of one inch. 
With I as a center, draw the circle H P T R. With the same 
radius (one inch ) draw the arcs with centers at A, B, C and 
D. Also draw the semi-circles with centers at L, F, M and E. 
Now draw the arcs as shown having centers at the centers of the 
small squares A L I E, L B F I, etc. To locate the centers of 
the six small circles Avithin the circle H P T R, draw a circle 
with a radius of inch and having the center in I. The small 
circles have a radius of inch. 

Inking. In inking this plate, the outlines of the squares of 
the various figures are inked only in Figs. 2 and 3. In Fig. 1 the 
only lines to be inked are those shown in full lines in PLATE 
III. First ink the star and then the square and diamonds. Tha 
cross hatching should be done without measuring the distance be¬ 
tween the lines and without the aid of any cross hatching device 
as this is an exercise for practice. The lines should be about ^ 
inch apart. After inking erase all construction lines. 

In inking Fig. 2 be careful not to run over lines. Each 
line should coincide with the pencil line. The student should 



88 


MECHANICAL DRAWING. 


first ink the horizontal lines L, M and N and the vertical lines 
E, F and G. The short lines should have the same width 
hut the border lines, A B, B C, C D and D A should be a 
little heavier. 

Fig. 3 is drawn entirely with the 45-degree triangle. In ink¬ 
ing the oblique lines make P I, R lv, T M, etc., a light distinct 
line. The alternate lines O II, Q J, S L, etc., should be some¬ 
what heavier. All of the lines which slope in the opposite direc¬ 
tion are light. After inking Fig. 3 all horizontal and vertical 
lines (except the border lines) should be erased. The border 
lines should be slightly heavier than the light oblique lines. 

The only instrument used in inking Fig. 4 is the compasses. 
In doing this exercise adjust the legs of the compasses so that the 
pen will always be perpendicular to the paper. If this is not 
done both nibs will not touch the paper and the line will be ragged. 
In inking the arcs, see that the pen stops exactly at the diagonals. 
The circle passing through T and the small inner circle should be 
dotted as.shown in PLATF III. After inking the circles and 
arcs erase the construction lines that are without the outer circles 
but leave in jpencil the diagonals inside the circle. 

In Fig. 5 draw all arcs first .and then draw the straight lines 
meeting these arcs. It is much easier to draw straight lines meet¬ 
ing arcs, or tangent to them, than to make the arcs tangent to 
straight lines. As this exercise is difficult .and in all mechanical 
and machine drawing arcs and tangents are frequently used we 
advise the beginner to draw this exercise several times. Leave 
all construction lines in pencil. 

Fig. 6 , like Fig. 4, is an exercise with compasses. If Fig. 6 
has been laid out accurately in pencil, the inked arcs will be tan¬ 
gent to each other and the finished exercise will have a good 
appearance. If, however, the distances were not accurately 
measured and the lines carefully drawn the inked arcs will not be 
tangent. The arcs whose centers are L, E, M and E and A, B, C 
and D should be heavier than the rest. The small circles may be 
drawn with the bow pen. After inking the arcs all construction 
lines should be erased. 









































MECHANICAL DRAWING. 

PART II. 

GEOflETRICAL DEFINITIONS. 

A point is used for marking position; it lias neither length 
breadth nor thickness. 

A line has length only; it is produced by the motion of a 
point. 

A straight line or right line is one that has the same direction 
throughout. It is the shortest distance between any two of its 
points. 

A curved line is one that is constantly changing in direction, 
It is sometimes called a curve. 

A broken line is one made up of several straight lines. 

Parallel lines are equally distant from each other at all 
points. 

A horizontal line is one having the direction of a line drawn 
upon the surface of water that is at rest. It is a line parallel to 
the horizon. 

A vertical line is one that lies in the direction of a thread 
suspended from its upper end and having a weight at the lower 
end. It is a line that is perpendicular to a horizontal plane. 

Lines are perpendicular to each other, if when they cross, 
the four angles formed are equal. If they meet and form two 
equal angles they are perpendicular. 

An oblique line is one that is neither vertical nor horizontal. 

In Mechanical Drawing, lines drawn along tne edge of the 
T square, when the head of the T square is resting against the 
left-hand edge of the board, are called horizontal lines. Those 
drawn at right angles or perpendicular to the edge of the T square 
are called vertical. 

If two lines cut each other, they are called intersecting lines , 
and the point at which they cross is called the point of intersection . 


40 


MECHANICAL DRAWING. 


ANGLES. 

An angle is formed when two straight lines meet. An angle 
is often defined as being the difference in direction of two straight 
lines. The lines are called the sides and the point of meeting is 
called the vertex. The size of an angle depends upon the amount 
of divergence of the sides and is independent of the length of 
these lines. 

Y_ 

BIGHT ANGLE. ACUTE ANGLE. OBTUSE ANGLE. 

If one straight line meet another and the angles thus formed 
are equal they are right angles. When two lines are perpendic¬ 
ular to each other the angles formed are right angles. 

An acute angle is less than a right angle. 

An obtuse angle is greater than a right angle. 

SURFACES. 

A surface is produced by the motion of a line; it has two 
dimensions, —length and breadth. 

A plane figure is a plane bounded on all sides by lines; the 
space included within these lines (if tl:ey are straight lines) is 
called a polygon or a rectilinear figure . 

TRIANGLES. 

A triangle is a figure enclosed by three straight lines. It is 
a polygon of three sides. The bounding lines are the sides , and 
the points of intersection of the sides are the vertices. The angles 
of a triangle are the angles formed by the sides. 

A right-angled triangle, often called a right triangle, is one 
that has a right angle. 

An acute-angled triangle is one that has all of its angles acute. 

An obtuse-angled triangle is one that has an obtuse angle. 

In an equilateral triangle all of the sides are equal. 









M KCIIA NICA L DRAWING. 


If all of the angles of a triangle are equal, the figure is called 


an equiangular triangle. 

A triangle is called scalene, when no two of its sides are 


equal. 

In an isosceles triangle two of the sides are equal. 



RIGHT ANGLED TRIANGLE. ACUTE ANGLED TRIANGLE. 


OBTUSE ANGLED TRIANGLE. 


The base of a triangle is the lowest side ; however, any side 
may he taken as the base. In an isosceles triangle the side which 
is not one of the equal sides is usually considered the base. 

The altitude of a triangle is the perpendicular drawn from 
the vertex to the base. 



A 



EQUILATERAL TRIANGLE. 


ISOSCELES TRIANGLE. 


SCALENE TRIANGLE. 


QUADRILATERALS. 


A quadrilateral is a plane figure bounded by four straight 

lines. 

The diagonal of a quadrilateral is a straight line joining two 
opposite vertices. 



TRAPEZOID. 


PARALLELOGRAM. 


QUADRILATERAL. 


A trapezium is a quadrilateral, no two of whose sides are 



A trapezoid is a quadrilateral having two sides parallel. 




















42 


MECHANICAL DRAWING. 


The bases of a trapezoid are its parallel sides. The altitude 
is the perpendicular distance between the bases. 

A parallelogram is a quadrilateral whose opposite sides are 
parallel. 

The altitude of a parallelogram is the perpendicular distance 
between the bases which are the parallel sides. 

There are four kinds of parallelograms: 


RECTANGLE. 


A rectangle is a parallelogram, all of whose angles are right 
angles. The opposite sides are equal. 

A square is a rectangle, all of whose sides are equal. 

A rhombus is a parallelogram which has four equal sides; 
but the angles are not right angles. 

A rhomboid is a parallelogram whose adjacent sides are 
unequal; the angles are not right angles. 

POLYGONS. 

A polygon is a plane figure bounded by straight lines. 

The boundary lines are called the sides and the sum of the 
sides is called the perimeter . 

Polygons are classified according to the number of sides. 

A triangle is a polygon of three sides. 

A quadrilateral is a polygon of four sides. 

A pentagon is a polygon of five sides. 

A hexagon is a polygon of six sides. 

A heptagon is a polygon of seven sides. 

An octagon is a polygon of eight sides. 

A decagon is a polygon of ten sides. 

A dodecagon is a polygon of twelve sides. 

An equilateral polygon is one all of whose sides are equal. 

An equiangular polygon is one all of whose angles are equal. 
A regular polygon is one all of whose angles are equal and all 
^f whose sides are equal. 







MECHANICAL DRAWING. 


43 


CIRCLES. 


A circle is a plane figure bounded by a curved line, every point 
of which is equally distant from a point within called the center. 

The curve which bounds the circle is called the circumference 
Any portion of the circumference is called an arc. 

The diameter of a circle is a straight line drawn through the 
center and terminating in the circumference. A radius is a 
straight line joining the center with the circumference. It has a 
length equal to one half the diameter. All radii (plural of 
radius) are equal and all diameters are equal since a diameter 
equals two radii. 



PENTAGON. 


X - \ 



An arc equal to one-half the circumference is called a *emi- 
circumference , and an arc equal to one-quarter of the circumfer¬ 
ence is called a quadrant. A quadrant may mean the sector, arc 
or angle. 

A chord is a straight line joining the extremities of an arc. 
It is a line drawn across a circle that does not pass through the 
center. 

A secant is a straight line which intersects the circumference 
in two points. 





A tangent is a straight line which touches the circumference 
at only one point. It does not intersect the circumference. The 
point at which the tangent touches the circumference is called the 
point of tangency or point of contact . 












44 


MECHANICAL DRAWING, 


A sector of a circle is the portion or area included between 
an arc and two radii drawn to the extremities of the arc. 

A segment of a circle is the area included between an arc 
and its chord. 

Circles are tangent when the circumferences touch at only 
one point and are concentric when they have the same center. 


■CONCENTRIC CIRCLES. INSCRIBED POLYGON 




An inscribed angle is an angle whose vertex lies in the cir¬ 
cumference and whose sides are . chords. It is measured by one- 
half the intercepted arc. 

A central angle is an angle whose vertex is at the center of 
the circle and whose sides are radii. 



An inscribed polygon is one whose vertices lie in the circum¬ 
ference and whose sides are chords. 


MEASUREMENT OF ANGLES. 

To measure an angle describe an arc with the center at the 
vertex of the angle and having any convenient radius. The por¬ 
tion of the arc included between the sides of the angle is the 
measure of the angle. If the arc has a constant radius the greater 
the divergence of the sides, the longer will be the arc. If there 
are several arcs drawn with the same center, the intercepted arcs 
will have different lengths but they will all be the same fraction 
of the entire circumference. 

In order that the size of an angle or arc may be stated with- 







MECHANICAL DRAWING. 


45 


out saying that it is a certain fraction of a circumference, the cir¬ 
cumference is divided into 360 
equal parts called degrees. Thus 
we can say that an angle contains 
45 degrees, which means that it is 
tWQ - 1 a circumference. In 
order to obtain accurate measure¬ 
ments each degree is divided into 
60 equal parts called minutes and 
each minute is divided into 60 equal 
parts called seconds . Angles and 
arcs are usually measured by means of an instrument called a 
protractor which has already been explained. 



SOLIDS. 

A polyedron is a solid bounded by planes. The bounding 
planes are called the faces and their intersections edges. The 
intersections of the edges are called vertices. 

A polygon having four faces is called a tetraedron ; one having 
six faces a hexaedron ; of eight faces an octaedron; of twelve- 
faces a dodecaedron, etc. 



PRISM. 


< > i 



RIGHT PRISM. 



TRUNCATED PRISM. 


A prism is a polyedron, of which two opposite faces, called 
bases, are equal and parallel; the other faces, called lateral faces 
are parallelograms. 

The area of the lateral faces is called the lateral area. 

The altitude of a prism is the perpendicular distance between 
the bases. 

Prisms are triangular , quadrangular , etc., according to the 
shape of the base. 

A right prism is one whose lateral edges are perpendicular 
to the bases. 

















46 


MECHANICAL DRAWING. 


A regular prism is a right prism having regular polygons for 
bases. 

A parallelopiped is a prism whose bases are parallelograms. 
If the edges are all perpendicular to the bases it is called a right 
parallelopiped. 

A rectangular parallelopiped is a right parallelopiped whose 

bases are rectangles ; all the faces are rectangles. 

PARALLELOPIPED. RECTANGULAR PARALLELOPIPED. OCTAEDRON. 




A cube is a rectangular parallelopiped all of whose faces are 
squares. 

A truncated prism is the portion of a prism included between 
the base and a plane not parallel to the base. 


PYRAMIDS. 

A pyramid is a polyedron one face of which is a polygon 
(called the base) and the other faces are triangles having a com¬ 
mon vertex. 



PYRAMID. 



REGULAR PYRAMID, 



FRUSTUM OF PYRAMID. 


The vertices of the triangles form the vertex of the pyramid. 
The altitude of the pyramid is the perpendicular distance 
from the vertex to the base. 

A pyramid is called triangular, quadrangular, etc., accord¬ 
ing to the shape of the base. 

A regular pyramid is one whose base is a regular polygon 























MECHANICAL DRAWING. 


47 


and whose vertex lies in the perpendicular erected at the center 
of the base. 

A truncated pyramid is the portion of a pyramid included 
between the base and a plane not parallel to the base. 

A frustum of a pyramid is the solid included between the 
base and a plane parallel to the base. 

The altitude of a frustum of a pyramid is the perpendicular 
distance between the bases. 

CYLINDERS. 

A cylindrical surface is a curved surface generated by the 
motion of a straight line which touches a curve and continues 
parallel to itself. 

A cylinder is a solid bounded by a cylindrical surface and 
two parallel planes intersecting this surface. 

The parallel faces are called *■ ases. 



CYLINDER. RIGHT CYLINDER. INSCRIBED CYLINDER. 


The altitude of a cylinder is the perpendicular distance 
between the bases. 

A circular cylinder is a cylinder whose base is a circle. 

A right cylinder or a cylinder of revolution is a cylinder gen¬ 
erated by the revolution of a rectangle about one side as an axis. 

A prism whose base is a regular polygon may be inscribed in 
or circumscribed about a circular cylinder. 

The cylindrical area is call the lateral area. The total area 
is the area of the bases added to the lateral area. 

CONES. 

A conical surface is a curved surface generated by the 
motion of a straight line, one point of which is fixed and the end 
Ok ends of which move in a curve. 

















48 


MECHANICAL DRAWING. 


A cone is a solid bounded by a conical surface and a plane 
which cuts the conical surface. 

The plane is called the base and the curved surface the 
lateral area. 

The vertex is the fixed point. 

The altitude of a cone is the perpendicular distance from the 
vertex^to the base.. N 

An element of a cone is a straight line from the vertex to the 
perimeter of the base. 

A circular cone is a cone whose base is a circle. 





FRUSTUM OF CONE. 


A right circular cone or cone of revolution is a cone whose 
axis is perpendicular to the base. It may be generated by the 
revolution of a right triangle about one of the perpendicular sides 
as an axis. 

A frustum of a cone is the solid included between the base 
and a plane parallel to the base. 





The altitude of a frustum of a cone is the perpendicular 
distance between the bases. 

SPHERES. 

A sphere is a solid bounded by a curved surface, every point 
of which is equally distant from a point within called the center. 
The radius of a sphere is a straight line drawn from the 









MECHANICAL DRAWING. 


49 


center to the surface. The diameter is a straight line drawn 
through the center and having its extremities in the surface. 

A sphere may be generated by the revolution of a semi-circle 
about its diameter as an axis. 

An inscribed polyedron is a polyedron whose vertices lie in 
the surface of the sphere. 

An circumscribed polyedron is a polyedron whose faces are 
tangent to a sphere. 

A great circle is the intersection of the spherical surface ana 
a plane passing through the center of a sphere. 

A small circle is the intersection of the spherical surface and 
a plane which does not pass through the center. 

A sphere is tangent to a plane when the plane touches the 
surface in only one point. A plane perpendicular to the extremity 
of a radius is tangent to the sphere. 

CONIC SECTIONS. 

If a plane intersects a cone the geometrical figures thus 
formed are called conic sections. A plane perpendicular to the 
base and passing through the vertex of a right circular cone forms 
an isosceles triangle. If the plane is parallel to the base the 
intersection of the plane and conical surface will be the circum¬ 
ference of a circle. 



Ellipse. The ellipse is a curve formed by the intersection of 
a plane and a cone, the plane being oblique to the axis but not 
cutting the base. If a plane is passed through a cone as shown 
in Fig. 1 or through a cylinder as shown in Fig 2, the curve of 
intersection will be an ellipse. An ellipse may be defined as 
being a curve generated by a point moving in a plane , the sum of 
the distances of the point to two fixed points being always constant . 

The two fixed points are called the foci and lie on the 

























50 


MECHANICAL DRAWING. 


longest line that can be drawn in the ellipse. One of these points 
is called a focus . 

The longest line that can be drawn in an ellipse is called the 
major axis and the shortest line, passing through the center, is 
called the minor axis. Tlie minor axis is perpendicular to the 
middle point of the major axis and the point of intersection is 
called the center 

An ellipse may be constructed if the major and minor axes 
are given or if the foci and one axis are known. 



Parabola. The parabola is a curve formed by the inter¬ 
section of a cone and a plane parallel to an element as shown in 
Fig. 3. The curve is not a closed curve. The branches approach 
parallelism. 

A parabola may be defined as being a curve every point of 
which is equally distant from a line 
and a point. 

The point is called the focus and 
the given line the directrix. The 
line perpendicular to the directrix 

and passing through the focus is 

the axis. The intersection of the 
axis and the curve is the vertex. 

Hyperbola. This curve is formed 
by the intersection of a plane and a cone, the plane being parallel 

to the axis of the cone as shown in Fig. 4. Like the parabola, 

the curve is not a closed curve; the branches constantly diverge. 

An hyperbola is defined as being a plane curve such that the 
difference of the distances from any point in the curve to two fixed 
points is equal to a given distance . 









MECHANICAL DRAWING. 


51 


The two fixed points are the foci and the line passing through 
them is the transverse axis. 

Rectangular Hyperbola. The form of hyperbola most used 
in Mechanical Engineering is called the rectangular hyperbola 
because it is drawn with reference to rectangular co-ordinates. 
This curve is constructed as follows : In Fig. 5, O X and O Y are 
the two co-ordinates drawn at right angles to each other. These 
lines are also called axes or 
asymptotes. Assume A to 
be a known point on the 
curve. In drawing this curve 
for the theoretical indicator 
card, this point A is the point 
of cut-off. 

Draw A C parallel to 
O X and A D perpendicular 
to O X. Now mark off any 5 ‘ 

convenient points on A C such as E, F, G, and H ; and through 
these points draw EE', FF', GG', and HH' perpendicular to O X. 
Connect E, F, G, H and C with O. Through the points of inter¬ 
section of the oblique lines and the vertical line AD draw the 
horizontal lines LL', MM', NN', PP' and QQ'. The first point on 
the curve is the assumed point A, the second point is R, the 
intersection of LL' and EE'. The third is the intersection S 
of MM' and FF'; the fourth is the intersection T of NN' and 
GG'. The other points are found in the same way. 

In this curve the products of the co-ordinates of all points are 
equal. Thus LR X RE' = MS X SF'= NT X TG'. 



Xj/' yy\ 

Y y 


/ 

siLi 





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ODONTOIDAL CURVES. 


The outlines of the teeth of gears must be drawn accurately 
because the smoothness of running depends upon the shape of the 
teeth. The two classes of curves generally employed in drawing 
gear teeth are the cycloidal and involute. 

Cycloid. The cycloid is a curve generated by a point on the 
circumference of a circle which rolls on a straight line tangent to 
the circle. 

The rolling circle is called the describing or generating circle 



















52 


MECHANICAL DRAWING. 


and the point, the describing or generating point . The tangent 
along which the circle rolls is called the director. 

In order that the curve may be a true cycloid the circle must 
roll without any slipping. 



Epicycloid. If the generating circle rolls upon the outside 
of an arc or circle, called the director circle , the curve thus gener¬ 
ated is called an epicycloid. The method of drawing this curve 
is the same as that for the cycloid. 

Hypocycloid. In case the generating circle rolls upon the 
inside of an arc or circle, the curve thus generated is called the 
hypocycloid. The circle upon which the generating circle rolls is 




called the director circle. If the generating circle has a diameter 
equal to the radius of the director circle the hypocycloid becomes 
a straight line. 

Involute. If a thread or fine wire is wound around a 
cylinder or circle and then unwound, the end will describe a 
curve called an involute. The involute may be defined as being 
a curve generated by a point in a tangent rolling on a circle known 
as the base circle. 

The construction of the ellipse, parabola, hyperbola and 
odontoidal curves will be taken up in detail with the plates. 









MECHANICAL DRAWING. 


PLATE IV. 

Pencilling. The horizontal and vertical center lines and the 
border lines for PLATE IV should he laid out in the same 
manner as were those for PL A TE I. There are to be six figures 
on this plate and to facilitate the laying out of the work, the fol¬ 
lowing lines should he drawn: measure off 2^ inches on both sides 
of the vertical center line and through these points draw vertical 
lines as shown in dot and dash lines on PLATFj IV In these 
six spaces the six figures are to be drawn, the student placing 
them in the centers of the spaces so that they will present a good 
appearance. In locating the figures, they should be placed a little 
above the center so that there will be sufficient space below to 
number the problem. 

The figures of the problems should first be drawn lightly in 
pencil and after the entire plate is completed the lines should be 
inked. In pencilling, all intersections must be formed with great 
care as the accuracy of the results depends upon the pencilling. 
Keep the pencil points in good order at all times and draw lines 
exactly through intersections. 

GEOMETRICAL PROBLEMS. 

The following problems are of great importance to the 
mechanical draughtsman. The student should solve them with 
care; he should not do them blindly, but should understand them 
so that he can apply the principles in later work. 

PROBLEM I. To Bisect a Given Straight Line. 

Draw the horizontal straight line A G about 3 inches long. 
With the extremity A as a center and any convenient radius 
(about 2 inches) describe arcs above and below the line A C. 
With the other extremity C as a center and with the same radius 
draw short arcs above and below A C intersecting the first arcs at 
D and E. The radius of these arcs must be greater than one-half 
the length of the line in order that they may intersect. Now 
draw the straight line I) E passing through the intersections D 
and E. This line cuts the line A C at F which is the middle 
point. 


AF = FC 



54 


MECHANICAL DRAWING. 


Proof. Since the points D and E are equally distant from 
A and C a straight line drawn through them is perpendicular to 
A C at its middle point F. 

PROBLEM 2. To Construct an Angle Equal to a Given 
Angle. 

Draw the line O C about 2 inches long and the line O A of 
about the same length. The angle formed b} r these lines may be 
any convenient size (about 45 degrees is suitable). This angle 
A O C is the given angle. 

Now draw F G a horizontal line about 21 inches long and let 
F the left-hand extremity be the vertex of the angle to be 
constructed. 

With O as a center and any convenient radius (about 1| 
inches) describe the arc L M cutting both O A and OC. With 
F as a center and the same radius draw the indefinite arc O Q. 
Now set the compass so that the distance between the pencil and 
the needle point is equal -to the chord L M. With Q as a center 
and a radius equal to L M draw an arc cutting the arc O Q at P. 
Through F and P draw the straight line F E. The angle E F G 
is the required angle since it is equal to A O C. 

Proof. Since the chords of the arcs L M and P Q are equal 
the arcs are equal. The angles are equal because with equal 
radii equal arcs are intercepted by equal angles. 

PROBLEM 8. To Draw Through a Given Point a Line 
Parallel to a Given Line. 

First Method . Draw the horizontal straight line A C about 
inches long and assume the point P about 1|- inches above 
A C. Through the point P draw an oblique line F E forming 
any convenient angle with A C. (Make the angle about 60 
degrees). Now construct an angle equal to P F C having the 
vertex at P and one side the line E P. (See problem 2). 
This may be done as follows: With F as a center and any con¬ 
venient radius, describe the arc L M. With the same radius 
draw the indefinite arc N O using P as the center. With N as a 
center and a radius equal to the chord L M, draw an arc cutting 
the arc N O at O. Through the points P and O draw a straight 
line which will be parallel to A C. 








































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.PLATE JJZ 



JANUARY IP, . /'jO 7 HERBERT CHANELER CHICAGO, ILL. 














































































































MECHANICAL DRAWING. 


55 


Proof. If two straight lines are cut by a third making the 
corresponding angles equal, the lines are parallel. 

PROBLEM 4. To Draw Through a Given Point a Line 
Parallel to a Given Line. 

Second Method. Draw the straight line A C about 3J inches 
long and assume the point P about 1-t inches above A C. With 
P as a center and any convenient radius (about 2T inches) draw 
the indefinite arc E D cutting the line A C. Now with the same 
radius and with D as a center, draw an arc P Q. Set the com¬ 
pass so that the distance between the needle point and the pencil 
is equal to the chord P Q. With D as a center and a radius 
equal to P Q, describe an arc cutting the arc E D at H. A line 
drawn through P and H will be parallel to A C. 

Proof. Draw the line Q H. Since the arcs P Q and H D 
are equal and have the same radii, the angles P H Q and H Q D 
are equal. Two lines are parallel if the alternate interior angles 
are equal. 

PROBLEM 5. To Draw a Perpendicular to a Line from 
a Point in the Line. 

First Method. When the point is near the middle of the line. 

Draw the horizontal line A C about 3|- inches long and 
assume the point P near the middle of the line. With P as a 
center and any convenient radius (about 1^ inches) draw two arcs 
cutting the line A C at E and F. Now with E and F as centers 
and any convenient radius (about 2i inches) describe arcs inter¬ 
secting at O. The line O P will be perpendicular to A C at P. 

Proof. The points P and O are equally distant from E and 
F. Hence a line drawn through them is perpendicular to the 
middle point of E F which is P. 

PROBLEM 6. To Draw a Perpendicular to a Line from 
a Point in the Line. 

Second Method. When the point is near the end of the line. 

Draw the line A 0 about 3£ inches long. Assume the given 
point P to be about -J inch from the end A. With any point D 
as a center and a radius equal to D P, describe an arc, cutting A C 
at E. Through E and D draw the diameter E O. A line from 
O to P is perpendicular to A C at P. 




5G 


MECHANICAL DRAWING. 


Proof. The angle 0 P E is inscribed in a semi-circle; hence 
it is a right angle, and the sides O P and P E are perpendicular 
to each other. 

After completing these figures draw pencil lines for the 
lettering. The words “PLATE IV” and the date and name 
should be placed in the border, as in preceding plates. To 
letter the words “ Problem 1,” “ Problem 2,” etc., draw horizontal 
lines | inch above the horizontal center line and the lower border 
line. Draw another line T 3 g inch above, to limit the height of the 
P, b and l. Draw a third line inch above the lower line as a 
guide line for the tops of the small letters. 

Inking. In inking PLATE IV the figures should be inked 
first. The line A C of Problem 1 should be a full line as it is 
the given line ; the arcs and line D E, being construction lines 
should be dotted. In Problem 2, the side.s of the angles should* 
be full lines. Make the chord L M and the arcs dotted, since 
as before, they are construction lines. 

In Problem 8, the line A C is the given line and P O is the 
line drawn parallel to it. As E E and the arcs do not form a part 
of the problem but are merely construction lines, drawn as an aid 
in locating P O, they should be dotted. In Problems 4, 5 and 6, 
the assumed lines and those found by means of the construction 
lines should be full lines. The arcs and construction lines should 
be dotted. In Problem 6, the entire circumference need not be 
inked, only that part is necessary that is used in the problem. 
The inked arc should however be of sufficient length to pass 
through the points O, P and E. 

After inking the figures, the border lines should be inked 
with a heavy line as before. Also, the words “ PLATE IV” and 
the date and the student’s name. Under each problem the words 
“Problem 1,” “Problem 2,” etc., should be inked; lower case let¬ 
ters being used as shown. 

PLATE V. 

Pencilling. In laying out the border lines and centre lines 
follow the directions given for PLATE IV. The dot and 
dash lines should be drawn in the same manner as there are to be 
six problems on this plate. 






























* 






































































PLATE 



JANUARY /9, /90 7 HERBERT CHANDLER CHICAGO, /LL. 



























































































MECHANICAL DRAWING. 


57 


PROBLEM 7. To Draw a Perpendicular to a Line from a 
Point without the Line. 

Draw the horizontal straight line A C about 3J inches long. 
Assume the point P about l} y inches above the line. With P as 
a center and any convenient radius (about 2 inches) describe an 
arc cutting A C at E and F. The radius of this arc must always 
be such that it will cut A C in two points; the nearer the points 
E and F are to A and C, the greater will be the accuracy of the 
work. Now with E and F as centers and any convenient radius 
(about 2^ inches) draw the arcs intersecting below A C at T. A 
line through the points P and T will be perpendicular to A C. 

In case there is not room below A C to draw the arcs, they 
may be drawn intersecting above the line as shown at N. When¬ 
ever convenient, draw the arcs below A C for greater accuracy. 

Proof. Since P and T are equally distant from E and F, 
the line P T is perpendicular to A C. „ 

PROBLEM 8. To Bisect a Given Angle. 

First Method. When the sides intersect. 

Draw the lines O C and O A forming any angle (from 45 to 
60 degrees). These lines should be about 3 inches long. With 
O as a center and any convenient radius (about 2 inches) draw 
an arc intersecting the sides of the angle at E and F. With E 
and F as centers and a radius of 1^ or 1| inches, describe short 
arcs intersecting at I. A line O D, drawn through the points O 
and I, bisects the angle. 

In solving this problem the arc E F should not be too near 
the vertex if accuracy is desired. 

Proof. The central angles A O D and DOC are equal 
because the arc E F is bisected by the line O D. The point I is 
equally distant from E and F. 

PROBLEM 9. To Bisect a Given Angle, 

Second Method. When the lines do not intersect. 

Draw the lines A C and E F about 4 inches long and in the 
positions as shown on PLATE V. Draw A! C and E'F' parallel 
to A C and E F and at such equal distances from them that 
they will intersect at O. Now bisect the angle C' O F' by 





58 


MECHANICAL DRAWING. 


the method of Problem 8. Draw the arc G H and with G and H 
as centers draw the arcs intersecting at R. The line O R bisects 
the angle. 

Proof. Since A' O' is parallel to A C and E' F' parallel to 
E F, the angle C r O F' is equal to the angle formed by the lines 
A C and E F. Hence as O R bisects angle C' O F' it also bisects 
the angle formed by the lines A C and E F. 

PROBLEM 10. To Divide a Given Line into any Number 
of Equal Parts. 

Let A C, about 3|- inches long, be the given line. Let us 
divide it into 7 equal parts. Draw the line A J at least 4 inches 
long, forming any convenient angle with A C. On A J layoff, 
by means of the dividers or scale, points D, E, F, G, etc., each 1 inch 
apart. If dividers are used the spaces need* not be exactly i 
inch. Draw the line J C and through the points D, E, F, G, etc., 
draw lines parallel to J C. These parallels will divide the line 
A C into 7 equal parts. 

Proof. If a series of parallel lines, cutting two straight 
lines, intercept equal distances on one of these lines, they also 
intercept equal distances on the other. 

PROBLEM 11. To Construct a Triangle having given the 
Three Sides. 

Draw the three sides as follows: 

A O', 2| inches long. 

E F, li| inches long. 

M N, 2^g inches long. 

Draw R S equal in length to A C. With R as a center and 
a radius equal to E F describe an arc. With S as a center and 
a radius equal to M N draw an arc cutting the arc previously 
drawn, at T. Connect T with R and S to form the triangle. 

PROBLEM 12. To Construct a Triangle having given 
One Side and the Two Adjacent Angles. 

Draw the line M N 8J- inches long and draw two angles 
A O D and E F G. Make the angle A O D about 80 degrees and 
E F G about 60 degrees. 

Draw R S equal in length to M N and at R construct an 



MECHANICAL DRAWING. 


59 


angle equal to A O D. At S construct an angle equal to E F G 
by the method used in Problem 2. PLATE V shows the neces¬ 
sary arcs. Produce the sides of the angles thus constructed 
until they meet at T. The triangle R T S will be the required 
triangle. 

After drawing these six figures in pencil, draw the pencil 
lines for the lettering. The lines for the words “ PLATE V i” 
date and name, should be pencilled as explained on page 20. 
The words “Problem 7,” “Problem 8,” etc., are lettered as for 
PLATE IV. 

Inking. In inking PLATE V, the same principles should 
be followed as stated with PLATE IV. The student should 
apply these principles and not make certain lines dotted just 
because they are shown dotted in PLATE V. 

After inking the figures, the border lines should be inked 
and the lettering inked as already explained in connection with 
previous plates. 


PLATE VI. 

Pencilling. Lay out this plate in the same manner as the 
two preceding plates. 

PROBLEM 18. To describe an Arc or Circumference 
through Three Given Points not in the same straight line. 

Locate the three points A, B and C. Let the distance 
between A and B be about 2 inches and the distance between A 
and C be about 2| inches. Connect A and B and A and C. 
Erect perpendiculars to the middle points of A B and A C. This 
may be done as explained with Problem 1. With A and B as 
centers and a radius of about 1| inches, describe the arcs inter¬ 
secting at I and J. With A and C as centers and with a radius 
of about 1J inches draw the arcs, intersecting at E and F. Now 
draw light pencil lines connecting the intersections I and J and 
E and F. These lines will intersect at O. 

With O as a center and a radius equal to the distance O A, 
describe the circumference passing through A, B and C. 

Proof. The point O is equally distant from A, B and C, 
since it lies in the perpendiculars to the middle points of A B and 



60 


MECHANICAL DRAWING. 


A C. Hence the circumference will pass through A, B and C. 

PROBLEM 14. To inscribe a Circle in a given Triangle. 

Draw the triangle L M N of any convenient size. M N may 
be made 3^ inches, L M, 2| inches, and L N, 31 inches. Bisect 
the angles M L N and L M N. The bisectors M I and L J may 
be drawn by the method used in Problem 8. Describe the arcs 
A C and E F, having centers at L and M respectively. The arcs 
intersecting at I and J are drawn as already explained. The 
bisectors of the angles intersect at O, which is the center of the 
inscribed circle. The radius of the circle is equal to the perpen¬ 
dicular distance from O to one of the sides. 

Proof. The point of intersection of the bisectors of the 
angles of a triangle is equally distant from the sides. 

PROBLEM 15. To inscribe a Regular Pentagon in a given 
Circle. 

With O as a center and a radius of about 1J inches, describe 
the given circle. With the T square and triangles draw the cen¬ 
ter lines A C and E F. These lines should be perpendicular to 
each other and pass through O. Bisect one of the radii, such as 
O C, and with this point H as a center and a radius H E, describe 
the arc E P. This arc cuts the diameter A C at P. With E as 
a center and a radius E P, draw arcs cutting the circumference 
at L and Q. With the same radius and a center at L, draw the 
arc, cutting the circumference at M. To find the point N, use 
either M or Q as a center and the distance E P as a radius. 

The pentagon is completed by drawing the chords E L, L M, 
M N, N Q and Q E. 

PROBLEM 16. To inscribe a Regular Hexagon in a given 
Circle. 

With 0 as a center and a radius of 1| inches draw the given 
circle. With the T square draw the diameter A D. With D as 
a center, and a radius equal to O D, describe arcs cutting the 
circumference at C and E. Now with C and E as centers and 
the same radius, draw the arcs, cutting the circumference at B 
and F. Draw the hexagon by joining the points thus formed. 

To inscribe a regular hexagon in a circle mark off chords 
equal in length to the radius. 


















































3.'1 V7<3 



JANUARY' 29. /90 7 HERBERT CHANBLER CH/CAGO. /LG 


















































































































MECHANICAL DRAWING. 


61 


To inscribe an equilateral triangle in a circle the same method 
may be used. The triangle is formed by joining the opposite 
vertices of the hexagon. 

Proof. The triangle O C D is an equilateral triangle by 
construction. Then the angle C O D is one-tliird of two right 
angles and one-sixth of four right angles. Hence arc C D is one- 
sixth of the circumference and the chord is a side of a regular 
hexagon. 

PROBLEM 17. To draw a line Tangent to a Circle at a 
given point on the circumference. 

With O as a center and a radius of about 1^ inches draw 
the given circle. Assume some point P on the circumference 
Join the point P with the center O and through P draw a line 
F P perpendicular to P O. This may be done in any one of several 
methods. Since P is the extremity of O P the method given in 
Problem 6 of PLATE IV, may be used. 

Produce P O to Q. With any center C, and a radius C P 
draw an arc or circumference passing through P. Draw E F a 
diameter of the circle whose center is C and through F and P 
draw the tangent. 

Proof. A line perpendicular to a radius at its extremity is 
tangent to the circle. 

PROBLEM 18. To draw a line Tangent to a Circle from a 
point outside the circle. 

With O as a center and a radius of about 1 inch draw the 
given circle. Assume P some point outside of the circle about 
21 inches from the center of the circle. Draw a straight line 
passing through P and O. Bisect P O and with the middle 
point F as a center describe the circle passing through P and O. 
Draw a line through P and the intersection of the two circum¬ 
ferences C. The line P C is tangent to the given circle. Simi¬ 
larly P E is tangent to the circle. 

Proof. The angle P C O is inscribed in a semi-circle and 
hence is a right angle. Since P C O is a right angle P C is per¬ 
pendicular to C O. The perpendicular to a radius at its extremity 
is tangent to the circumference. 

Inking. In inking PLATE VI the same method should be 



MECHANICAL DRAWING. 


62 


followed as in previous plates. The name and address should be 
lettered in inclined Gothic capitals as before. 

PLATE VII. 

Pencilling. PLATE VII should be laid out in the same 
manner as previous plates. Six problems on the ellipse, spiral, 
parabola and hyperbola are to be constructed in the six spaces. 

PROBLEM 19. To draw an Ellipse when the Axes are 
given. 

Draw the lines L M and C D about 3| and 2^ inches long 
respectively. Let C D be perpendicular to M N at its middle 
point P. Make C P = P D. These two lines are the axes. With 
C as a center and a radius equal to one-half the major axis or 
equal to L P, draw the arc, cutting the major. axis at E and F. 
These two points are the foci. Now mark off any convenient 
distances on P M, such as A, B and G. 

With E as a center and a radius equal to L A, draw arcs 
above and below L M. With F as a center, and a radius equal 
to A M describe short arcs cutting those already drawn as shown 
at N. With E as a center and a radius equal to L B draw arcs 
above and below L M as before. With JT as a center and a radius 
equal to B M, draw arcs intersecting those already drawn as shown 
at O. The point P and others are found by repeating the process. 
The student is advised to find at least 12 points on the curve — 
6 above and 6 below L M. These 12 points with L, C, M and 
D will enable the student to draw the curve. 

After locating these points, a free hand curve passing through 
them should be sketched. 

PROBLEM 20. To draw an Ellipse when the two Axes are 
given. 

Second Method . Draw the two axes A B and P Q in the 
same manner as for Problem 19. With O as a center and a radius 
equal to one-half the major axis, describe the circumference A C 
D E F B. Similarly with the same center and a radius equal to 
one-half the minor axis, describe a circle. Draw any radii such 
as O C, O D, O E, O F, etc., cutting both circumferences. These 
radii may be drawn with the 60 and 45 degree triangles. At the 









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EEBRUARY 4. /90 7 HERBERT CHANDLER CH/CAGO, /LL 














































































































































































MECHANICAL DRAWING. 


63 


points of intersection of the radii with the large circle C D E and 
F, draw vertical lines and from the intersection of the radii wit! 
the small circle C', D', E', and F', draw horizontal lines intersect¬ 
ing the vertical lines. The intersections of these lines are points 
on the curve. 

As in Problem 19, a free hand curve should be sketched pass¬ 
ing through these points. About five points in each quadrant 
will be sufficient. 

PROBLEM 21. To draw an Ellipse by means of a 
Trammel. 

As in the two preceding problems, draw the major and minor 
axes, U V and X Y. Take a slip of paper having a straight 
edge and mark off 0 B equal to one-half the major axis, and D B 
one-half the minor axis. Place the slip of paper in various 
positions keeping the point D on the major axis and the point C 
on the minor axis. If this is done the point B will mark various 
points on the curve. Find as many points as necessary and sketch 
the curve. 

PROBLEM 22. To draw a Spiral of one turn in a circle. 

Draw a circle with the center at O and a radius of li inches. 
Mark off on the radius O A, distances of one-eighth inch. As 
O A is 1J inches long there will be 12 of these distances. Draw 
circles through these points. Now draw radii O B, O C, O D 
etc. each 30 degrees apart (use the 30 degree triangle). This 
will divide the circle into 12 equal parts. The curve starts at the 
center O. The next point is the intersection of the line 0 B and 
the first circle. The third, point is the intersection of O C and 
the second circle. The fourth point is the intersection of O D 
and the third circle. Other points are found in the same way. 
Sketch in pencil the curve passing through these points. 

PROBLEM 23. To draw a Parabola when the Abscissa and 
Ordinate are given. 

Draw the straight line A B about three inches long. This 
line is the axis or as it is sometimes called the abscissa. At A 
and B draw lines perpendicular to A B. Also with the T square 
draw E C and F D, 1| inches above and below A B. Let A be 




04 


MECHANICAL DRAWING. 


the vertex of the parabola. Divide A E into any number of 
equal parts and divide E C into the same number of equal parts. 
Through the points of division, R, S, T, U and V, draw horizontal 
lines and connect L, M, N, O and P, with A. The intersections 
of the horizontal lines-with the oblique lines are points on the 
curve. For instance, the intersection of A L and the line V is 
one point and the intersection of A M and the line U is another. 

The lower part of the curve A D is drawn in the same 
manner. 

PROBLEM 24. To draw a Hyperbola when the abscissa 
E X, the ordinate A E and the diameter X Y are given. 

Draw E F about 3 inches long and mark the point X, 1 inch 
from E and the point Y, 1 inch from X G With the triangle and 
T square, draw the rectangles A B D C and O P Q R* such that 
A B is 1 inch in length and A C, 3 inches in length. Divide 
A E into any number of equal parts and A B into the same num¬ 
ber of equal parts. Draw L X, M X and N X; also connect T, 
U and Y with Y. The first point on the curve is the intersection 
A; the next is the intersection of T Y and L X ; the third the 
intersection of U Y and M X. The remaining points are found 
in the same manner. The curve X C and the right-hand curve 
P Y Q are found by repeating the process. 

Inking. In inking the figures on this plate, use the French 
or irregular curve and make full lines for the curves and their 
axes. The construction lines should be dotted. Ink in all the 
construction lines used in finding one-half of a curve, and in 
Problems 19, 20, 23 and 24 leave all construction lines in pencil 
except those inked. In Problems 21 and 22 erase all construction 
lines not inked. The trammel used in Problem 21 may be drawn 
in the position as shown, or it may be drawn outside of the ellipse 
in any convenient place. 

The same lettering should be done on this plate as on previous 
plates. 

PLATE VIII. 

Pencilling. In laying out Plate VIII, draw the border lines 
and horizontal and vertical center lines as in previous plates, to 
divide the plate into four spaces for the four problems. 














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tube yj.v'icj 



FEBRUARY /2, /SO 7 HERBERT CHRNJJLER CH/CHGO, /LL. 


































































































































MECHANICAL DRAWING. 


Go 


PROBLEM 25. To construct a Cycloid when the diameter 
of the generating circle is given. 

With 0' as a center and a radius of | inch draw a circle, and 
tangent to it draw the indefinite horizontal straight line A B. 
Divide the circle into any number of equal parts (12 for instance) 
and through these points of division C, D, E, F, etc., draw hori¬ 
zontal lines. Now with the dividers set so that the distance 
between the points is equal to the chord of the arc C D, mark off 
the points L, M, N, O, P on the line A B, commencing at the 
point H. At these points erect perpendiculars to the center line 
G O'. This center line is drawn through the point O' with the 
T square and is the line of centers of the generating circle as it 
rolls along the line A B. Now with the intersections Q, R, S, 
T, etc., of these verticals with the center line as centers describe 
arcs of circles as shown. The points on the curve are the inter¬ 
sections of these arcs and the horizontal lines drawn through the 
points C, D, E, F, etc. Thus the intersection of the arc whose 
center is Q and the horizontal line through C is a point I on the 
curve. Similarly, the intersection of the arc whose center is R 
and the horizontal line through D is another point J on the curve. 
The remaining points, as well as those on the right-hand side, are 
found in the same manner. To obtain great accuracy in this 
curve, the circle should he divided into a large number of equal 
parts, because the greater the number of divisions the less the error 
due to the difference in length of a chord and its arc. 

PROBLEM 26. To construct an Epicycloid when the di¬ 
ameter of the generating circle and the diameter of the director 
circle are given. 

The epicycloid and hypocycloid may be drawn in the same 
manner as the cycloid if arcs of circles are used in place of the 
horizontal lines. With O as a center and a radius of | inch 
describe a circle. Draw the diameter E F of this circle and pro¬ 
duce E F to G such that the line F G is 2J inches long. With 
G as a center and a radius of 2| inches describe the arc A B of 
the director circle. With the same center G, draw the arc P Q 
which will be the path of the center of the generating circle as it 
rolls along the arc A B Now divide the generating circle into 





66 


MECHANICAL DRAWING. 


any number of equal parts (twelve for instance) and through the 
points of division H, I, L, M, and N, draw arcs having G as a 
center. With the dividers set so that the distance between the 
points is equal to the chord H I, mark off distances on the 
director circle A F B. Through these points of division R, S, 
T, U, etc., draw radii intersecting the arc P Q in the points IF, S', 
T', etc., and with these points as centers describe arcs of circles 
as in Problem 25. The intersections of these arcs with the arcs 
already drawn through the points H, I, L, M, etc., are points on 
the curve. Thus the intersection of the circle whose center is R' 
with the arc drawn through the point H is a point upon the curve. 
Also the arc whose center is S' with the arc drawn through the 
point I is another point on the curve. The remaining points are 
found by repeating this process. 

PROBLEM 27. To draw an Hypocycloid when the diam¬ 
eter of the generating circle and the radius of the director circle 
are given. 

With O as a center and a radius of 4 inches describe the arc 
E F, which is the arc of the director circle. Now with the same 
center and a radius of 3^ inches, describe the arc A B, which is the 
line of centers of the generating circle as it rolls on the director 
circle. With O' as a center and a radius of | inch describe the 
generating circle. As before, divide the generating circle into 
any number of equal parts (12 for instance) and with these points 
of division L, M, N, O, etc., draw arcs having O as a center. 
Upon the arc E F, lay off distances Q R, R S, S T, etc., equal to 
the chord Q L. Draw radii from the points R, S, T, etc., to the 
center of the director circle O and describe arcs of circles having a 
radius equal to the radius of the generating circle, using the 
points G, I, J, etc., as centers. As in Problem 26, the inter¬ 
sections of the arcs are the points on the curve. By repeating 
this process, the right-hand portion of the curve may be drawn. 

PROBLEM 28. To draw the Involute of a circle whan the 
diameter of the base circle is known. 

With point 0“ as a center and a radius of 1 inch, describe the 
base circle. Now divide the circle into any number of equal parts 
16 for instance) and connect the points of divisuHi with the cen- 



MECHANICAL DRAWING. 


07 


ter of the circle by drawing the radii 0 C, 0 D, O E. O F, etc., 
to O B. At the point D, draw a light pencil line perpendicular 
to the radius O I) This line will be tangent to the circle. 
Similarly at the points E, F, G, 11, etc., draw tangents to the 
circle. Now set the dividers so that the distance between the 
points will be equal to the chord of the arc C D, and measure this 
distance from D along the tangent. Beginning with the point E, 
me‘.sure on the tangent a distance equal to two of these chords, 
from the point F measure on the tangent three divisions, and from 
the point G measure a distance equal to four divisions on the 
tangent G P. Similarly, measure distances on the remaining 
tangents, each time adding the length of the chord. This will 
give the points Q, R, S and T. Now sketch a light pencil line 
through the points L, M, N, P, etc., to T. This curve will be the 
involute of the circle. 

Inking. The same rules are to be observed in inking PLATE 
VIII as were followed in the previous plates, that is, the curves 
should be inked in a full line, using the French or irregular curve. 
All arcs and lines used in locating the points on one-half of the 
curve should be inked in dotted lines. The arcs and lines used in 
locating the points of the other half of the curve may be left in 
pencil in Problems 25 and 26. In Problem 28, all construction 
lines should be inked. After completing the problems the same 
lettering should be done on this plate as on previous plates. 









































































































































































































MECHANICAL DRAWING. 

PART III. 


PROJECTIONS. 


ORTHOGRAPHIC PROJECTION. 

Orthographic Projection is the art of representing objects of 
three dimensions by views on two planes at right angles to each 
other, in such a way that the forms and positions may be completely 
determined. The two planes are called planes of projection or 
co-ordinate planes, one being vertical and the other horizontal, as 
shown in Fig. 1. These planes are sometimes designated V and H 
respectively. The intersection of V and H is known as the ground 
line G L. 

The view or projection of the figure on the plane gives the 
same appearance to the eye placed in a certain position that the 
object itself does. This position 
of the eye is at an infinite dist¬ 
ance from the plane so that the 
rays from it to points of a limited 
object are all perpendicular to the 
plane. Evidently then the view of 
a point of the object is on the plane 
and in the ray through the point 
and the eye or where this perpendicular to the plane pierces it. 

Let a , Fig. 1, be a point in space, draw a perpendicular from a 
to V. Where this line strikes the vertical plane, the projection of a 
is found, namely at a y . Then drop a perpendicular from a to the 
horizontal plane striking it at a h , which is the horizontal projection 
of the point. Drop a perpendicular from a y to H; this will 
intersect G L at o and be parallel and equal to the line a & h . In 
the same way draw a perpendicular from a h to V, this also will 
intersect G L at o and will be parallel and equal to a a y . In other 
words, the perpendicular to G L from the projection of a point on 
either plane equals the distance of the point from the other plane. 
B in Fig. 1, shows a line in space. B v is its V projection, and B b 















70 


MECHANICAL DRAWING 


its H projection, these being determined by finding views of points 
at its ends and connecting the points. 

Instead of horizontal projection and vertical projection, the 
terms plan and elevation are commonly nsed. 

Suppose a cube, one inch on a side, to be placed as in Fig. 2, 
with the top face horizontal and the front face parallel to the 
vertical plane. Then the plan will be a one-inch square, and the 
elevation also a one-inch square. In general the plan is a repre¬ 
sentation of the top of the object, and the elevation a view of the 
front. The plan then is a top view, and the elevation a front view. 




Thus far the two planes have been represented at right angles 
to each other, as they are in space. In order that they may be 
shown more simply and on the one plane of the paper, H is 
revolved about G L as an axis until it lies in the same plane as V 
as shown in Fig. 2. The lines l h O and 2 h N, being perpendicular 
to G L, are in the same straight line as 5 V O and 6 V N, which also 
are perpendicular to G L. That is —two views of a point are 
always in a line perpendicular to G L. From this it is evident 
that the plan must be vertically below the elevation, point for point. 
Now looking directly at the two planes in the revolved position, we 





















MECHANICAL DRAWING 


V 


get a true orthographic projection of the cube as shown in Fig. 3. 

All points on an object at the same height must appear in 
elevation at the same distance above the ground line. If numbers 
1, 2, 3, and 4 on the plan, Fig. 3, indicate the top corners of the 
cube, then these four points, being at the same height, must be 


4 V 3 V 

shown in elevation at the same height and at the top, p and -p 


The top of the cube, 1, 2,3,4, is shown in elevation as the straight line 
4 v 3 V 

-p ~ 2 v * This illustrates the fact that if a surface is perpendicular 


to either plane or projection, its projection on that plane is simply 
a line; a straight line if the surface is plane, a curved line if the 
surface is curved. From the same figure it is seen that the top 
edge of the cube, 1 4, has for its projection on the vertical plane 


4 V 

the point -p, the principle of 


which is stated in this way: If a 



Fig. 4. 


straigni cine is perpendicular to either V or H, its projection on 
that plane is a point, and on the other plane is a line equal in 
length to the line itself, and perpendicular to the qround line . 

Fig. 4 is given as an exercise to help to show clearly the idea 
of plan and elevation. 

A = a point B" above H, and A" in front of V. 

B = square prism resting on H, two of its faces parallel to V, 

C = circular disc in space parallel to V. 

D = triangular card in space parallel to V. 

E = cone resting on its base on H. 

F = cylinder perpendicular to V, and with one end resting against V. 

G = line perpendicular to H. 

H = triangular pyramid above H, with its base resting against V. 












72 


MECHANICAL DRAWING. 


Suppose in Fig. 5, that it is desired to construct the pro¬ 
jections of a prism li in. square, and 2 in. long, standing on one 
end on the horizontal plane, two of its faces being parallel to the 
vertical plane. In the first place, as the top end of the prism is a 
square, the top view or plan will be a square of the same size, 
that is, 1| in. Then since the prism is placed parallel to and in 
front of the vertical plane the plan, lj in. square, will have two 
edges parallel to the ground line. As the front face of the prism 


ELEVATION 

OR 

FRONT VIEW 



Fig. 5. 


is parallel to the vertical plane its projection on V will be a rect¬ 
angle, equal in length and width to the length and width respec¬ 
tively of the prism, and as the prism stands with its base on H, 
the elevation, showing height above H, must have its base on the 
ground line. Observe carefully that points in elevation are verti¬ 
cally over corresponding points in plan. 

The second drawing in Fig. 6 represents a prism of the same 
size lying on one side on the horizontal plane, and with the ends 
parallel to V. 

The principles which have been used thus far may be stated 
As follows, — 
















MECHANICAL DRAWING. 


73 


1. If a line or point is on either plane, its other projection 
must be in the ground line. 

2. Height above II is shown in elevation as height above 
the ground line, and distance in front of the vertical plane is shown 
in plan as distance from the ground line. 

3. If a line is parallel to either plane, its actual length is 
shown on that plane, and its other projection is parallel to the 
ground line. A line oblique to either plane has its projection on 
that plane shorter than the line itself, and its other projection 
oblique to the ground line. No projection can be longer than the 
line itself. 

4. A plane surface if parallel to either plane, is shown on 



Fig. 6. Fig. 7. 


that plane in its true size and shape; if oblique it is shown 
smaller than the true size, and if perpendicular it is shown as a 
straight line. Lines parallel in space must have their V projec¬ 
tions parallel to each other and also their H projections. 

If two lines intersect, their projections must cross, since the 
point of intersection of the lines is a point on both lines, and 
therefore the projections of this point must be on the projections 
of both lines, or at their intersection. In order that intersecting 
lines may be represented, the vertical projections must intersect 
in a point vertically above the intersection of the horizontal pro* 









74 


MECHANICAL HR AW ESC. 


jections. Thus Fig. 6 represents two lines which do intersect as 
O crosses D®at a point vertically above the intersection of C h and 
D fc . In Fig. 7, however, the lines do not intersect since the inten- 
sections of their projections do not lie in the same vertical line. 

In Fig. 8 is given the plan and elevation of a square pyramid 
standing on the horizontal plane. The height of the pyramid is 
the distance A B. The slanting edges of the pyramid, A C, A D, 
etc., must be all of the same length, since A is directly above the 

center of the base. What this length 
is, however, does not appear in either 
projection, as these edges are not 
parallel to either V or H. 

Suppose that the pyramid be 
turned around into the dotted posi¬ 
tion C, D, E, F, where the horizontal 
projections of two of the slanting 
edges, A C, and A E, are parallel to 
the ground line. These two edges, 
having their horizontal projections 
parallel to the ground line, are now 
parallel to V, and therefore their new 
vertical projections will show their 
true lengths. The base of the pyra¬ 
mid is still on H, and therefore is 
projected on V in the ground line. 
The apex is in the same place as be¬ 
fore, hence the vertical projection of 
the pyramid in its new position is shown by the dotted lines. The 
vertical projection A C, v is the true length of edge A C. Now if 
we wish to find simply the true length of A C, it is unnecessary to 
turn the whole pyramid around, as the one line A C will be sufficient. 

The principle of finding the true length of lines is this, anu 
can be applied to any case : Swing one projection of the line par¬ 
allel to the ground line, using one end as center. On the other 
projection the moving end remains at the same distance from the 
ground line, and of course vertically above or below the same end 
in its parallel position. This new projection of the line shows its 
true length. See the three Figures at the top of page 9. 













MECHANICAL DRAWING. 


75 


Third plane of projection or profile plane. A plane perpen¬ 
dicular to both co-ordinate planes, and hence to the ground line, is 



called a profile plane . This plane is vertical in position, and may 
be used as a plane of projection. A projection on the profile plane 
is called a profile view, or end view , or sometimes edge view, and 
is often required in machine or other drawing when the plan and 
elevation do not sufficiently give the shape and dimensions. 

A projection on this plane is found in the same way as on the 



V plane, that is, by perpendiculars drawn from points on the 
object. 

Since, however, the profile plane is perpendicular to the 
ground line, it will be seen from the front and top simply as a 


































7G 


MECHANICAL DRAWING. 


straight line; in order that the size and shape of the profile view 
may be shown, the profile plane is revolved into V using its inter¬ 
section with the vertical plane as the axis. 

Given in Fig. 9, the line A B by its two projections A v B w and 
A h B\ and given also the profile plane. Now by projecting the 
line on the profile by perpendiculars, the points A, v B’,* and B { h A, 71 
are found. Revolving the profile plane like a door on its hinges, all 
points in the plane will move in horizontal circles, so the horizontal 
projections A, 71 and B, 71 will move in arcs of circles with O as center 
to the ground line, and the vertical projections B t v and A, v will move 
in lines parallel to the ground line to positions directly above the 
revolved points in the ground line, giving the profile view of the 
line A p B p . Heights, it will be seen, are the same in profile view 

as in elevation. By referring to 
the rectangular prism in the same 
figure, we see that the elevation 
gives vertical dimensions and those 
parallel to V, while the end view 
shows vertical dimensions and 
those perpendicular to V. The 
profile view of any object may be 
found as shown for the line A B 
by taking one point at a time. 

In Fig. 10 there is repre¬ 
sented a rectangular prism or 
block, whose length is twice the 
width. The elevation shows its 
height. As the prism is placed at 
an angle, three of the vertical edges will be visible, the fourth 
one being invisible. 

In mechanical drawing lines or edges which are invisible are 
drawn dotted. The edges which in projection form a part of the 
outline or contour of the figure must always be visible, hence 
always full lines. The plan shows what lines are visible in eleva¬ 
tion, and the elevation determines what are visible in plan. In 
Fig. 10, the plan shows that the dotted edge A B is the back edge, 
and in Fig. 11, the dotted edge C D is found, by looking at the 
elevation, to be the lower edge of the triangular prism. In general, 



Fig. 10. 













MECHANICAL DRAWING. 


77 


if in elevation an edge projected within the figure is a back edge, 
it must be dotted, and in plan if an edge projected within the 
outline is a lower edge it is dotted. 

Fig. 12 is a circular cylinder with the length vertical and 



Fig. 11. 


with a hole part way through as shown in elevation. Fig. 13 is 
plan, elevation and end view of a triangular prism with a square 
hole from end to end. The plan and elevation alone would be 
insufficient to determine positively the shape of the hole, but the 
end view shows at a glance that it is square. 

In Fig. 14 is shown plan and elevation of the frustum of a 
square pyramid, placed with its base on the horizontal plane. If the 
frustum is turned through 30°, as shown in the plan of Fig. 15, 
the top view or plan must still be the same shape and size, and as 
the frustum has not been raised or lowered, the heights of all 
points must appear the same in elevation as before in Fig. 14. 
The elevation is easily found by projecting points up from the 
plan, and projecting the height of the top horizontally across from 
the first elevation, because the height does not change. 

The same principle is further illustrated in Figs. 1G and 17. 
The elevation of Fig. 1G shows a square prism resting on one edge, 
and raised up at an angle of 30° on the right-hand side. The 



















78 


MECHANICAL DRAWING. 


plan gives the width or thickness, | in. Notice that the length of 
the plan is greater than 2 in. and that varying the angle at 




which the prism is slanted would change the length of the plan. 
Now if the prism be turned around through any angle with the 
vertical plane, the lower edge still being on H, and the inclination 



Fig. 14. 



Fig. 15. 


of 30° with II remaining the same, the plan must remain the same 
size and shape. 

If the angle through which the prism be turned is 45°, we 

















































MECHANICAL DRAWING. 


79 


have the second plan, exactly the same shape and size as the first; 
The elevation is found by projecting the corners of the prism ver 



tically up to the heights of the same points in the first elevation. 
All the other points are found in the same way as point No. 1. 



Fig. 17. 

Three positions of a rectangular prism are shown in Fig. 17. 
Ln the first view, the prism stands on its base, its axis therefore 











































80 


MECHANICAL DRAWING. 


is parallel to the vertical plane. In the second position, the axis is 
still parallel to V and one corner of the base is on the horizontal 
plane. The prism has been turned as if on the line l h 1 V as an 
axis, so that the inclination of all the faces of the prism to the 
vertical plane remains the same as before. That is, if in the first 
figure the side A B C D makes an angle of 30° with the vertical, 
the same side in the second position still makes 30° with the ver¬ 



tical plane. Hence the elevation of No. 2 is the same shape and size 
as in the first case. The plan is found by projecting the corners 
down from the elevation to meet horizontal lines projected across 
from the corresponding points in the first plan. The third posi¬ 
tion shows the prism with all its faces and edges making the same 
angles with the horizontal as in the second position, but with the 
plan at a different angle with the ground line. The plan then is 
the same shape and size as in No. 2, and the elevation is found by 
projecting up to the same heights as shown in the preceeding 
elevation. This principle may be applied to any solid, whether 
bounded by plane surfaces or curved. 

This principle as far as it relates to heights, is the same that 
was used for profile views. An end view is sometimes necessary 
before the plan or elevation of an object can be drawn. Suppose 
that in Fig. 18 we wish to draw the plan and elevation of a tri¬ 
angular prism 3" long, the end of which is an equilateral triangle 











MECHANICAL DRAWING. 


81 


1^" on each side. The prism is lying on one of its three faces on 
II, and inclined toward the vertical plane at an angle of 80°. We 

are able to draw the plan at 
once, because the width will be 
inches, and the top edge will 
be projected half way between 
the other two. The length of 
the prism will also be shown. 
Before we can draw the elevation, 
we must find the height of the 
top edge. This height, however, 
must be equal to the altitude of 
the triangle forming the end of 
the prism. All that is necessary, 
then, is to construct an equilat¬ 
eral triangle on each side, and measure its altitude. 

A very convenient way to do this is shown in the figure by 
laying one end of the prism down on H. A similar construction 
is shown in Fig. 19, but with one face of the prism on V instead 
of on H. 

In all the work thus far the plan has been drawn below and 
the elevation above. This order is sometimes inverted and the 
plan put above the elevation, but the plan still remains a top view 
no matter where placed, so that after some practice it makes but 
little difference to the draughtsman which method is employed. 

SHADE LINES. 

It is often the case in machine drawing that certain lines or 
edges are made heavier than others. These heavy lines are called 
shade lines, and are used to improve the appearance of the draw¬ 
ing, and also to make clearer in some cases the shape of the 
object. The shade lines are not put on at random, but according 
to some system. Several systems are in use, but only that one 
which seems most consistent will be described. The shade lines 
are lines or edges separating light faces from dark ones, assuming 
the light always to come in a direction parallel to the dotted 
diagonal of the cube shown in Fig. 20. The direction of the 
light, then, may be represented on II by a line at 45° running 









82 


MECHANICAL DRAWING. 


backward to the right and on V by a 45° line sloping downward 
and to the right. Considering the cube in Fig. 20, if the light 
comes in the direction indicated, it is evident that the front, left- 
hand side and top will be light, and the bottom, back and right- 
hand side dark. On the plan, then, the shade lines will be the 
back edge 1 2 and the right-hand edge 2 3, because these edges 
are between light faces and dark ones. On the elevation* since 
the front is light, and the right-hand side and bottom dark, the edges 
3 7 and 8 7 are shaded. As the direction of the light is represented 
on the plan by 45° lines and on the elevation also by 45° lines, 




Fig. 20. 

we may use the 45° triangle with the T-square to determine 
the light and dark surfaces, and hence the shade lines. If 
the object stands on the horizontal plane, the 45° triangle is used 
on the plan, as shown in Fig. 21, but if the length is perpen¬ 
dicular to the vertical plane, the 45° triangle is used on the eleva¬ 
tion, as shown in Fig. 22. This is another way of saying that the 
45° triangle is used on that projection of the object which shows 
the end. By applying the triangle in this way we determine, the 
light and dark surfaces, and then put the shade lines between 
them. Dotted lines, however, are never shaded, so if a line 
which is between a light and a dark surface is invisible it is not 















MECHANICAL DRAWING. 


83 


shaded. In Fig. 21 the plan shows the end of the solid, hence the 
45° triangle is used in the direction indicated by the arrows. 

This shows that the light strikes the left-hand face, but not 
the back or the right-hand. The top is known to be light with- 



Fig. 21. Fig. 22. 


out the triangle, as the light comes downward, so the shade edges 
on the plan are the back and right-hand. On the elevation two 
faces of the prism are visible; one is light, the other dark, hence 
the edge between is shaded. The left-hand edge, being between 
a light face and a dark one is a shade line. The right-hand face 
is dark, the top of the prism is light, hence the upper edge of this 
face is a shade line. The right-hand edge is not shaded, because 
by referring to the plan, it is seen to be between two dark 
surfaces. In shading a cylinder or a cone the same rule is fol 
lowed, the only difference being that as the surface is curved, the 
light is tangent, so an element instead of an edge marks the 
separation of the dark from the light, and is not shaded. The 
elements of a cylinder or cone should never be shaded, but the 
bases may. In Fig. 23, Nos. 3 and 4, the student should carefully 
notice the difference between the shading of the cone and cylinder- 




















84 


MECHANICAL DRAWING. 


If in No. 4 the cone were inverted, the opposite half of the base 
would be shaded, for then the base would be light, whereas it is 
now dark. In Nos. 7 and 8 the shade lines of a cylinder and a 
circular hole are contrasted. 


In No. 7 it is clear that the light would strike inside on the 
further side of the hole, commencing half way where the 45° lines 




Fig. 23. 

are tangent. The other half of the inner surface would be dark, 
hence the position of the shade line. The shade line then enables 
us to tell at a glance whether a circle represents a hub or boss, or 
depression or hole. Fig. 24 represents plan, elevation and profile 
view of a square prism. Here as before, the view showing the 
end is the one used to determine the light and dark surfaces, and 
then the shade lines put in accordingly. 








































MECHANICAL DRAWING. 


8,5 


In putting on the shade lines, the extra width of line is put 
inside the figure, not outside. In shading circles, the shade line 
is made of varying width, as shown in the figures. The method 
of obtaining this effect by the compass is to keep the same radius, 
but to change the center slightly in a direction parallel to the rays 
of light, as shown at A and B in No. 2 of Fig. 24. 




Fig. 24. 

INTERSECTION AND DEVELOPHENT. 

If one surface meets another at some angle, an intersection is 
produced. Either surface may be plane, or curved. If both are 
plane, the intersection is a straight line; if one is curved, the 
intersection is a curve, except in a few special cases ; and if both 
are curved, the intersection is usually curved. 

In the latter case, the entire curve does not alw T ays lie in the 
same planes. If all points of any curve lie in the same plane, it 
is called a plane curve. A plane intersecting a curved surface 
must always give either a plane curve or a straight line. 

In Fig. 25 a square pyramid is cut by a plane A parallel to the 
horizontal. This plane cuts from the pyramid a four-sided figure^ 
the four corners of which will be the points where A cuts the four 
slanting edges of the solid. The plane intersects edge oh at point 4^ 
in elevation. This point must be found in plan vertically below on 















86 


MECHANICAL DRAWING. 


- - —-—%- 

the horizontal projection of line o 5, that is, at point 4A Edge 
o e is directly in front of o b, so is shown in elevation as the same 
line, and plane A intersects o e at point 1» in elevation, found in 
plan at 1A Points 3 and 2 are obtained in the same way. The 
intersection is shown in plan as the square 1 2 3 4, which is also 
its true size as it is parallel to the horizontal plane. In a 
q'' similar .way the sections are found 

in Figs. 26 and 27. It will be 
seen that in these three cases 
where the planes are parallel to 
the bases, the sections are of the 
same shape as the bases, and have 
their sides parallel to the edges of 
the bases. 

It is an invariable rule that 
when such a solid is cut by a plane 
parallel to its base, the section is 
a figure of the same shape as the 
base. If then in Fig. 28 a right 
cone is intersected by a plane 
parallel to the base the section 
must be a circle, the center of 
which in plan coincides with the apex. The radius must 
equal o d. 

In Figs. 29 and 30 the cutting plane is not parallel to the base, 
hence the intersection will not be of the same shape as the base. 
The sections are found, however, in exactly the same manner as 
in the previous figures, by projecting the points where the plane 
intersects the edges in elevation on to the other view of the same 
line. 

. i 

INTERSECTION OF PLANES WITH CONES OR CYLINDERS. 

Sections cut by a plane from a cone have already been de¬ 
fined as conic sections. These sections may be either of the fol¬ 
lowing: two straight lines, circle, ellipse, parabola, hyperbola. 
All except the parabola and hyperbola may also be cut from a 
cylinder. 

Methods have previously been given for constructing the 



Fig. 25. 















MECHANICAL DRAWING. 


87 

















































88 


MECHANICAL DRAWING. 


ellipse, parabola and hyperbola without projections; it will now 
be shown that they may be obtained as actual intersections. 

In Fig. 31 the plane cuts the cone obliquely. To find 
points on the curve in plan take a series of horizontal planes 



Fig. 31. 


x y z etc., between points c v and d v . One of these planes, as 2 V. 
should be taken through the center of c d. The points c and d 
must be points on the curve, since the plane cuts the two contoui 
elements at these points. The horizontal projections of the contoui 
elements will be found in a horizontal line passing through the center 
of the base; hence the horizontal projection of c and d will be 
found on this center line, and will be the extreme ends of the 
curve. Contour elements are those forming the outline. 




















MECHANICAL DRAWING. 


89 


The plane x cuts the surface of the cone in a circle, as it is 
parallel to the base, and the diameter of the circle is the distance 
between the points where x crosses the two contour elements. 
This circle, lettered x on the plan, lias its center at the horizontal 
projection of the apex. The circle x and the curve cut by the plane 
are both on the surface of the cone, and their vertical projec¬ 
tions intersect at the point 2. Also the circle x and the curve 
must cross twice, once on the front of the cone and once on the 
back. Point 2 then represents two points which are shown in 
plan directly beneath on the circle x, and are points on the re¬ 
quired intersection. Planes y and z, and as many more as may 
be necessary to determine the curve accurately, are used in the 
same Avay. The curve found is an ellipse. The student will 
readily see that the true size of this ellipse is not shown in the 
plan, for the plane containing the curve is not parallel to the 
horizontal. 

In order to find the actual size of the ellipse, it is necessary 
to place its plane in a position parallel either to the vertical or to 
the horizontal. The actual length of the long diameter of the 
ellipse must be shown in elevation, c*> dv, because the line is 
parallel to the vertical plane. The plane of the ellipse then may 
be revolved about cv d» as an axis until it becomes parallel to Y, 
Avhen its true size Avill be shown. For the sake of clearness of 
construction,* cv d° is imagined moved over to the position c' d\ 
parallel to dv. The lines 1—1, 2—2, 3—3 on the plan show the 
true width of the ellipse, as these lines are parallel to H, but are 
projected closer together than their actual distances. In elevation 
these lines are shown as the points 1, 2, 3. at their true distance 
apart. Hence if the ellipse is revolved around its axis cv dv, the 
distances 1—1, 2—2, 3—3 will appear perpendicular to cv dv, and 
the true size of the figure be shown. This construction is made on 
the left, where 1'—1', 2'—2' and 3'—S' are equal in length to 1—1, 
2—2, 3—3 on the plan. 

In Fig. 32 a plane cuts a cylinder obliquely. This is a 
simpler case, as the horizontal projection of the curve coincides 
with the base of the cylinder. To obtain the true size of the 
section, which is an ellipse, any number of points are assumed on 
the plan and projected up on the cutting plane, at 1, 2, 3, etc. 



90 


Mechanical drawing. 


The lines drawn through these points perpendicular to 1 7 are 
made equal in length to the corresponding distances 2'—2 r , 3'—3' 
etc.j on the plan, because 2'—2' is the true width of curve at 2. 

If a cone is intersected by a plane which is parallel to only 

one of the elements, as in 
Fig. 33, the resulting curve 
is the parabola, the construc¬ 
tion of which is exactly simi¬ 
lar to that for the ellipse as 
given in Fig. 31. If the 
intersecting plane is parallel 
to more than one element, or 
is parallel to the axis of the 
cone, a hyperbola is produced. 

In Fig. 34, the vertical 
plane A is parallel to the axis 
of the cone. In this instance 
the curve when found will 
appear in its true size, as 
plane A is parallel to the 
vertical. Observe that the 
highest point of the curve is 
found by drawing the circle 
X on the plan tangent to the 
given plane. One of the 
points where this circle crosses 
tl^e diameter is projected up 
to the contour element of the 
cone, and the horizontal plane X drawn. Intermediate planes 
Y, Z, etc., are chosen, and corresponding circles drawn in plan. 
The points where these circles are crossed by the plane A are 
points on the curve, and these points are projected up to the 
elevation on the planes Y, Z, etc. 

DEVELOPflENTS. 

The development of a surface is the true size and shape ot 
the surface extended or spread out on a plane. If the surface to 
be developed is of such a character that it may be flattened out 














mechanical drawing. 


01 


without tearing or folding, we obtain an exact development, as in 
case of a cone or cylinder, prism or pyramid. If this cannot be 
done, as with the sphere, the development is only approximate. 

In order to find the development of the rectangular prism in 
Fig 35, the back face, 1 2 7 6, is supposed to be placed in contact 



Fig. 33. 


with some plane, then the prism turned on the edge 2 7 until the 
side 2 3 8 7 is in contact with the same plane, then this continued 
until all four faces have been placed on the same plane. The 
rectangles 1 4 3 2 and 6 7 8 5 are for the top and bottom respec¬ 
tively. The development then is the exact size and shape of a 
covering for the prism. If a rectangular hole is cut through the 
prism, the openings in the front and back faces will be shown in 
the development in the centers of the two broad faces. 

The development of a right prism, then, consists of as many 














92 


MECHANICAL DRA WING. 


rectangles joined together as the prism has sides, these rectangles 
being the exact size of the faces of the prism, and in addition two 
n polygons the exact size of the bases. It will be found helpful in 
developing a solid to number or letter all of the corners on the 

projections, then 
designate each face 
when developed in 
the same way as in 
the figure. 

If a cone be 
placed on its side on 
a plane surface, one 
element will rest on 
the surface. If now 
the cone be rolled on 
the plane, the vertex 
remaining stationary, 
until the same ele¬ 
ment is in contact 
again, the space rolled 
over will represent 
the development of 
the convex surface 
of the cone. A, Fig. 
86, is a cone cut by a 
plane parallel to the 
base. In B, let the 
vertex of the cone be 
placed at V, and one element of the cone coincide with V A I. 
The length of this element is taken from the elevation A, of 
either contour element. All of the elements of the cone are of 
the same length, so when the cone is rolled each point of the base 
as it touches the plane will be at the same distance from the 
vertex. From this it follows that the development of the base 
will be the arc of a circle of radius equal to the length of an 
element. To find the length of this arc which is equal to the 
distance around the base, divide the plan of the circumference 
of the base into any number of equal parts, a* twelve, then 























MECHANICAL DRAWING. 


93 


with the length of one of these parts as radius, lay off twelve 
spaces, 1....13, join 1 and 13 with Y, and the sector is the development 
of the cone from vertex to base. To represent on the development 



the circle cut by the section plane, take as radius the length of 
the element from the vertex to D, and witli Y as center describe 




an arc. The development of the frustum of the cone will be the 
portion of the circular ring. This of course does not include the 




























94 


MECHANICAL DRAWING. 


development of the bases, which would lie simply two circles the 
same sizes as shown in plan. 

A and B, Fig. 3T, represent the plan and elevation of a 
regular triangular pyramid and its development. If face C is 
placed on the plane its true size will be shown at C in the devel¬ 
opment. The true length of the base of triangle C is shown in 
the plan. The slanting edges, however, not being parallel to the 
vertical, are not .shown in elevation in their true length. It be¬ 
comes necessary then, to find the true length of one of these edges 
as shown in Fig. 6, after which the triangle may be drawn in its 
full size at C in the development. As the pyramid is regular, 
three equal triangles as shown developed at C, D and E, together 
with the base F, constitute the development. 

If a right circular cylinder is to be developed, or rolled upon 
a plane, the elements, being parallel, will appear as parallel lines, 




and the base, being perpendicular to the elements, will develop as 
a straight line perpendicular to the elements. The width of the 
development will be the distance around the cylinder, or the cir¬ 
cumference of the base. The base of the cylinder in Fig. 38, is 
divided into twelve equal parts, 12 3, etc.. Commencing at point 
1 on the development these twelve equal spaces are laid along 
the straight line, giving the development of the base of the cylin¬ 
der, and the total width. To find the development of the curve 
cut by the oblique plane, draw in elevation the elements corre¬ 
sponding to the various divisions of the base, and note the points 








MECHANICAL DRAWING. 


95 


where they intersect the oblique plane. As Ave roll the cylinder 
beginning at point 1, the successive elements 1, 12, 11, etc., will 
appear at equal distances apart, and equal in length to the lengths 
of the same elements in elevation. Thus point number 10 on the 
development of the curve is found by projecting horizontally across 
from 10 in elevation. It will be seen that the curve is symmetri¬ 
cal, the half on the left of T being similar to that on the right. 
The development of any curve whatever on the surface of the 
cylinder may be found in the same manner. 

The principle of cylinder development is used in laying out 
elbow joints, pipe ends cut off obliquely, etc. In Fig. 39 is shown 
plan aud elevation of a three-piece elbow and collar, and develop¬ 



ments of the four pieces. In order to construct the various parts 
making up the joint, it is necessary to know what shape and size 
must be marked out on the flat sheet metal so that when cut out 
and rolled up the three pieces will form cylinders with the ends 
fitting together as required. Knowing the kind of elbow desired, 
we first draw the plan and elevation, and from these make the 
developments. Let the lengths of the three pieces A, B and C 
be the same on the upper outside contour of the elbow, the piece 
B at an angle of 45°; the joint between A and B bisects the 
angle between the two lengths, and in the same way the joint 
between B and C. The lengths A and C will then be the same, 






















96 


MECHANICAL DRAWING. 


and one pattern will answer for both. The development of A 
is made exactly as just explained for Fig. 38, and this is also the 
development of C. 

It should be borne in mind that in developing a cylinder we 
must always have a base at right angles to the elements, and if 
the cylinder as given does not have such a base, it becomes neces¬ 
sary to cut the cylinder by a plane perpendicular to the elements, 
and use the intersection as a base. This point must be clearly 
understood in order to proceed intelligently. A section at right 
angles to the elements is the only section which will unroll in a 



straight line, and is therefore the section from which we must 
work in developing other sections. As B has neither end at right 
angles to its length, the plane X is drawn at the middle and per¬ 
pendicular to the length. B is the same diameter pipe as C and 
A, so the section cut by X will be a circle of the same diameter 
as the base of A, and its development is shown at X. 

From the points where the elements drawn on the elevation 
of A meet the joint between A and B, elements are drawn on B, 






















































MECHANICAL DRAWING. 


97 


which are equally spaced around B the same as on A. The spaces 
then laid off along X are the same as given on the plan of A. 
Commencing with the left-hand element in B, the length of the 
upper element between X and the top corner of the elbow is laid 
off above X, giving the first point in the development of the end 
of B fitting with C. The lengths of the other elements in the 
elevation of B are measured in the same way and laid off from *X. 
The development of the 
other end of the piece 
B is laid off below X, 
using the same distances, 
since X is Half way be¬ 
tween the ends. The 
development of the 
' collar is simply the de. 
velopment of the frus¬ 
tum of a cone, which has 
already been explained, 

Fig. 86. The joint be¬ 
tween B and C is shown 
in plan as an ellipse, the 
construction of which 
the student should be 
able to understand from 
a study of the figure. 

The intersection of 
a rectangular prism and 
pyramid is shown in Fig. 40. The base b c d e of the pyramid is 
shown dotted in plan, as it is hidden by the prism. All four edges 
of the pyramid pass through the top of the prism, 1, 2, 8, 4. As 
the top of the prism is a horizontal plane, the edges of the pyramid 
are shown passing through the top in elevation at x v g*> lev iv. These 
four points might be projected to the plan on the four edges of the 
pyramid; but it is unnecessary to project more than one, since the 
general principle applies here that if a cone, p} r ramid, prism or 
cylinder be cut by a plane parallel to the base, the section is a 
figure parallel and similar to the base. The one point x*> is there¬ 
fore projected down to a b in plan, giving xh, and with this as 























98 


MECHANICAL DRAWING. 


one corner, the square xh gh i h kh is drawn, its sides parallel to the 
edges of the base. This square is the intersection of the pyramid 
with the top of the prism. 

The intersection of the pyramid with the bottom of the prism 
is found in like manner, by taking the point where one edge of 
the pyramid as a b passes through the bottom of the prism shown 
in elevation as point m®, projecting down to mh on ah bh, and 
drawing the square mh nh oh ph parallel to the base of the pyramid. 
These two squares constitute the entire intersection of the two 
solids, the pyramid going through the bottom and coming out at 
the top of the prism. As much of the slanting edges of the 



pyramid as are above the prism will be seen in plan, appearing as 
the diagonals of the small square, and the rest of the pyramid, 
being below the top surface of the prism, will be dotted in plan. 

Fig. 41 is the development of the rectangular prism, show¬ 
ing the openings in. the top and bottom surfaces through which 
the pyramid passed. The development of the top and bottom, 
back and front faces will be four rectangles joined together, the 
same sizes as the respective faces. Commencing with the bottom 
face 5 6 7 8, next would come the back face 6127, then the top, 
etc. The rectangles at the ends of the top face 1 2 8 4 are the 
ends of the prism. These might have been joined on any other 












MECHANICAL DRAWING. 


99 


face as well. Now find the development of the square in the bottom 
5 6 7 8. As the size will be the same as in projection, it only re¬ 
mains to determine its position. This position, however, will 
have the same relation to the sides of the rectangle as in the plan. 
The center of the square in this case is in the center of the face. 
To transfer the diagonals of the square to the development, extend 
them in plan to intersect the edges of the prism in points 9, 10, 
11 and 12. Take the distance from 5 to 9 along the edge 5 6, 
and lay it on the development from 5 along 5 6, giving point 9. 
Point 10 located in the same way and connected with 9, gives the 
position of one diagonal. The other diagonal is obtained in a 
similar way, then the square constructed on these diagonals. The 
same method is used for locating the small square on the top face. 

If the intersection of a cylinder and prism is to be found, we 
may either obtain the points where elements of the cylinder pierce 
the prism, or where edges and lines parallel to edges on the sur¬ 
face of the prism cut the cylinder. 

A series of parallel planes may also be taken cutting curves 
from the cylinder and straight lines from the prism; the intersec¬ 
tions give points on the intersection of the two solids. 

Fig. 42 represents a triangular prism intersecting a cylinder. 
The axis of the prism is parallel to V and inclined to H. Starting 
with the size and shape of the base, this is laid off at a, b h c h , and 
the altitude of the triangle taken and laid off at a v c v in elevation, 
making right angles with the inclination of the axis to H. The 
plan of the prism is then constructed. To find the intersection of 
the two solids, lines are drawn on the surface of the prism parallel 
to the length and the points where these lines and the edges 
pierce the cylinder are obtained and joined, giving the curve. 

The top edge of the prism goes into the top of the cylinder. 
This point will be shown in elevation, since the top of the cylinder 
is a plane parallel to H and perpendicular to V, and therefore 
projected on V as a straight line. The upper edge, then, is found 
to pass into the top of the cylinder at point 0 , o v and o h . The 
intersection of the two upper faces of the prism with the top of 
the cylinder will be straight lines drawn from point 0 and will be 
shown in plan. If we can find where another line of the surface 
0 a b 14 pierces the upper base of the cylinder, this point joined 


1.0FC* 




Fig. 43. 


100 


MECHANICAL DRAWING. 


with o will determine the intersection of this face with the top of 
the cylinder. A surface may always be produced, if necessary, 
to find an intersection. 


Edge a b pierces the plane of the top of the cylinder at point 



d, seen in elevation; therefore the line joining this point with o is 
the intersection of one upper face of the -prism with the upper 


Fig. 42. 





































MECHANICAL DRAWING. 


101 


base of the cylinder. The only part of this line needed, of course, 
is within the actual limits of the base, that is o 9. The intersec¬ 
tion o 8 of the other top face is found by the same method. On 
the convex surface of the cylinder there will be three curves, one 
for each face of the prism. Points b and 9 on the upper base of 
the cylinder, will be where the curves for the two upper faces will 
begin. The point d is found on the revolved position of the base 
at dp and d, b is divided into the equal parts e, —/j, etc., 

which revolve back to d\ e h ,f h and g h . The divisions are made 
equal merely for convenience in developing. The vertical pro¬ 
jections of d, e, etc., are found on the vertical projection of a b, 
directly above d h , e h , etc., or may be found by taking from the 
revolved position of the base, the perpendiculars from d y e, etc., to 
c h b h and laying them off in elevation from b v along b v a v . Lines 
such as /12, m 5, etc., parallel to a o are drawn in plan and eleva¬ 
tion. Points i h k h m h n h are taken directly behind d h e h f h g h 
hence their vertical projections coincide. Points n l m l k { and are 
formed by projecting across from n h m h k h and i h . 

The convex surface of the cylinder is perpendicular to H, so 
the points where the lines on the prism pierce it will be projected 
on plan as the points where these lines cross the circle, 14, 13,12, 

11.3. The vertical projections of these points are found on 

the corresponding lines in elevation, and the curves drawn through. 
The curve 3, 4....8 must be dotted, as it is on the back of the 
cylinder. The under face of the prism, which ends with the line 
b c , is perpendicular to the vertical plane, so the curve of intersec 
tion will be projected on V as a straight line. Point 14 is one 
end of this curve. 3 the other end, and the curve is projected in 
elevation as the straight line from 14 to the point where the lower 
edge of the prism crosses the contour element of the cylinder. 

Fig. 43 gives the development of the right-hand half of the 
cylinder, beginning with number 1. As previously explained, the 
distance between the elements is shown in the plan, as 1—2, 2—3, 
3—4 and so on. These spaces are laid off in the development 
along a straight line representing the development of the base, 
and from these points the elements are drawn perpendicularly. 

The lengths of the elements in the development from the base 
to the curve are exactly the same as on the elevation, as the 







MECHANICAL DRAWING. 


l02 


slevation gives the true lengths. If then the development of the 
base is laid off along the same straight line as the vertical projec¬ 
tion of the base, the points in elevation ma}^ be projected across 
with the T-square to the corresponding elements in the develop¬ 
ment. The points on the curve cut by the under face of the 
prism are on the same elements as the other curves, and their 
vertical projections are on the under edge of the prism, hence 
these points are projected across for the development of the lower 
curve. 

In Fig. 44 is given the development of the prism from the 
right-hand end as far as the intersection with the cylinder, begin- 


14 



ning at the left with the top edge a o , the straight line a b c a 
being the development of the base. As this must be the actual 
distance around the base, the length is taken from the true size 
of the base, a { b h c h . The parallel lines drawn on the surfaces of 
the prism must appear on the development their true distances 
apart, hence the distances a, d r d { e p etc., are made equal to 
a d, d e , etc. on the development. The actual distances between the 
parallel lines on the bottom face of the prism are shown along 
the edge of the base, b h c h . Perpendicular lines are drawn from 
the points of division on the development. 

The position of the developed curve is found by laying off 
the true lengths on the perpendiculars. These true lengths (of 
the parallel lines) are not shown in plan, as the lines are not 
parallel to the horizontal plane, but are found in elevation. The 
length oa on the development is equal to a v d 10 to d v 10, and 


























MECHANICAL DRAWING 


103 


so on for all the rest. Point 9 is found as follows: on the projec¬ 
tions, the straight line from o to d passes through point 9, and the 
true distance from o to 9 is shown in plan. All that is necessary, 
then, is to connect o and d on the development, and lay off from o 
the distance o h 9. Number 8 is found in the same way. 

ISOMETRIC PROJECTION. 

Heretofore an object has been represented by two or more 
projections. Another system, called isometrical drawing, is used 
to show in one view the three dimensions of an object, length (or 
height), breadth, and thickness. An isometrical drawing of an 
object, as a cube, is called for brevity the “ isometric ” of the cube. 



Fig. 45. 


To obtain a view which shows the three dimensions in such a 
way that measurements can be taken from them, draw the cube in 
the simple position shown at the left of Fig. 45, in which 
it rests on H with two faces parallel to V; the diagonal from the 
front upper right-hand corner to the back lower left-hand corner is 
indicated by the dotted line. Swing the cube around until the 
diagonal is parallel with V as shown in the second position. Here 
the front face is at the right. In the third position the lower end 
of the diagonal has been raised so that it is parallel to H, becoming 
thus parallel to both planes. The plan is found by the principles 
of projection, from the elevation and the preceding plan. The front 
face is now the lower of the two faces shown in the elevation. 
From this position the cube is swung around, using the corner 
























104 


MECHANICAL DRAWING 


resting on the H as a pivot, until the diagonal is perpendicular 
to Y but still parallel to H. The plan remains the same, except as 
regards position; while the elevation, obtained by projecting across 
from the previous elevation, gives the isometrical projection of the 
cube. The front face is now at the left. 

In the last position, as one diagonal is perpendicular to V, it 
follows that all the faces of the cube make equal angles with V, 
hence are projected on that plane as equal parallelograms. For the 
same reason all the edges of the cube are projected in elevation in 
equal lengths, but, being inclined to V, appear shorter than they 
actually are on the object. Since they are all equally foreshortened 
and since a drawing may be made at any scale, it is customary to 

make all the isometrical lines of a 
drawing full length. This will give 
the same proportions, and is much 
the simplest method. Herein lies 
the distinction between an isomet¬ 
rical projection and an isometric 
drawing. 

It will be noticed that the 
figure can be inscribed in a circle, 
and that the outline is a perfect 
hexagon. Hence the lines showing 
breadth and length are 30° lines, 
while those showing height are 
vertical. 

Fig. 46 shows the isometric of a cube, 1 inch square. All of 
the edges are shown in their true length, hence all the surfaces 
appear of the same size. In the figure the edges of the base are 
inclined at 30° with a T-square line, but this is not always the case. 
For rectangular objects, such as prisms, cubes, etc., the base 
edges are at 30° only when the prism or cube is supposed to be in 
the simplest possible position. The cube in Fig. 46 is supposed to 
be in the position indicated by plan and elevation in Fig. 47, that 
is, standing on its base, with two faces parallel to the vertical 
plane. 

If the isometric of the cube in the position of Fig. 48 were 
required, it could not be drawn with the base edges at 30°; neither 









MECHANICAL DKAWING 


10 5 


would these edges appear in their true lengths. It follows, then, 
that in isometrical drawing, true lengths appear only as 30° lines 
or as vertical lines. Edges or lines that in actual projection are 
either parallel to the ground line or perioendicular to V, are drawn 
in isometric as 30° lines, full length; and those that are actually 
vertical are made vertical in isometric, also full length. 

In Fig. 45, lines such as the front vertical edges of the cube 
and the two base edges are called the three isometric axes. The 
isometric of objects in oblique positions, as in Fig. 48, can be con- 



Fig. 47. Fig. 48. 

structed only by reference to their projections, by methods which 
will be explained later. 

In isometric drawing small rectangular objects are more satis¬ 
factorily represented than large curved ones. In woodwork, mor- 
. tises and joints and various parts of framing are well shown in 
isometric. This system is used also to give a kind of bird’s-eye 
view of the mills or factories. It is also used in making sketches 
of small rectangular pieces of machinery, where it is desirable to 
give shape and dimensions in one view. 

In isometric drawing the direction of the ray of light is 
parallel to that diagonal of a cube which runs from the upper left 
corner to the lower right corner, as 4 V -7 V in the last elevation of 
Fig. 45. This diagonal is at 30°; hence in isometrical drawing 
the direction of the light is at 30° downward to the right. From 



















106 


MECHANICAL DRAWING 


this it follows that the top and two left-hand faces of the cube are 
light, the others dark. This explains the shade Jines in Fig. 45. 

In Fig. 45, the top end of the diagonal which is parallel to the 
ray of light in the first position is marked 4, and traced through 
to the last or isometrical projection, 4 V . It will be seen that face 
3 V 4 v 5 V 8 V of the isometric projection is the front face of the cube 
in the first view; hence we may consider the left front face of the 
isometric cube as the front. This is not absolutely necessary, 
but by so doing the isometric shade edges are exactly the same 
as on the original projection. 


f 



Fig. 49 shows a cube with circles inscribed in the top and 
two side faces. The isometric of a circle is an ellipse, the exact 
construction of which would necessitate finding a number of points; 
for this reason an approximate construction by arcs of circles is 
often made. In the method of Fig. 49, four centers are used. 
Considering the upper face of the cube, lines are drawn from the 
obtuse, angles/*and e, to the centers of the opposite sides. 

The intersections of these lines give points g and A, which 
serve as centers for the ends of the ellipse. With center g and 
radius g a , the arc a d is drawn; and with f as center and radius 
f d , the arc d c is described, and the ellipse finished by using 
centers h and e. This construction is applied to all three faces. 

Fig. 50 is the isometric of a cylinder standing on its base. 












mechanical drawing 


107 


Notice that the shade line on the top begins and ends where 
T-square lines would be tangent to the curve, and similarly in the 
case of the part shown on the base. The explanation of the shade 
is very similar to that in pro¬ 
jections. Given in projections 
a cylinder standing on its 
base, the plan is a circle, and 
the shade line is determined 
by applying the 45° triangle 
tangent to the circle. This is 
done because the 45° line is 
the projection of the ray of 
light on the plane of the 
base. 

In Fig. 49, the diagonal m l may represent the ray of light 
and its projection-on the base is seen to be Jc l , the diagonal of the 
base, a T-square line. Hence, for the cylinder of Fig. 50, apply 
tangent to the base and also to the top a line parallel to the 
projection of the ray of light on these planes, that is, a T-square 
line, and this will mark the beginning and ending of the shade line. 

In Fig. 49 the projection of the ray of light diagonal m l on 
the right-hand face is e Z, a 30° 
line; hence, in Fig. 51, where the 
base is similarly placed, apply 
the 30° triangle tangent as indi¬ 
cated, determining the shade line 
of the base. If the ellipse on 
the left-hand face of the cube were 
the base of a cone or cylinder 
Fl &- 52 * extending backward to the right, 

the same principle would be used. 

The projection of the cube diagonal m l on that face is m n , a 
60° line; hence the 60° triangle would be used tangent to the base 
in this last supposed case, giving the ends of the shade line at 
points o and r. Figs. 52, 53 and 54 illustrate the same idea with 
respect to prisms, the direction of the projection of the ray of light 
on the plane of the base being used in each case to determine the 
light and dark faces and hence the shade lines. 






108 


MECHANICAL DKAWING 



In Fig. 52 a prism is represented standing on its base, so that 
the projection of the cube diagonal on the base (that is, a T-square 
line) is used to determine the light and dark faces as shown. 

The prism in Fig. 53 has for 
its base a trapezium. The 
projection of the ray of light 
on this end is parallel to the 
diagonal of the face; hence 
the 60° triangle applied par¬ 
allel to this diagonal shows 
that faces a c db and a g hi) 
are light, while c e f d and 
g e f h are dark, hence the 
shade lines as shown. 

The application in Fig. 
54 is the same, the only 
difference being in the position of the prism, and the consequent 
difference in the direction of the diagonal. 

Fig. 55 represents a block with smaller blocks projecting from 
three faces. 

Fig. 56 shows a framework of three pieces, two at right angles 
and a slanting brace. The horizontal piece is mortised into the 
upright, as indicated by the 
dotted lines. In Fig. 57 
the isometric outline of a 
house is represented, show¬ 
ing a dormer window and 
a partial hip roof; a b is a 
hip rafter, c d a valley. Let 
the pitch of the main roof 
be shown at B, and let m be 
the middle point of the top 
of the end wall of the 
house. Then, by measuring 
vertically up a distance m l 
equal to the vertical height 



Fig. 54. 


a n shown at B, a point on the line of the ridge will be found at l. 
Line l i is equal to b A, and i h is then drawn. Let the pitch of 








MECHANICAL DRAWING 


•109 


the end roof be given at A. This shows that the peak of the roof, 
or the end a of the ridge, will be back from the end wall a distance 
equal to the base of the triangle at A. Hence lay 61f from l this 
distance, giving point and join a with b and x. 



The height k e of the ridge of the dormer roof is known, and 
we must find where this ridge will meet the main roof. The ridge 
must be a 30° line as it runs parallel to the end wall of the house 

















110* 


MECHANICAL DRAWING 


and to the ground. Draw from e a line parallel to b A to meet a 
vertical through A at f. This point is in the vertical plane of the 
end wall of the house, hence in the plane of i h. If now a 80° line 
be drawn from/'parallel to x b, it will meet the roof of the house 
at g. The dormer ridge and f g are in the same horizontal plane, 
hence will meet the roof at the same distance below the ridge a i. 
Therefore draw the 80° line g c , and connect c with d . 

In Fig. 58 a box is shown with the cover opened through 150°. 



The right-hand edge of the bottom shows the width, the left-hand 
edge the length, and the vertical edge the height. The short edges 
of the cover are not isometric lines, hence are not shown in their 
true lengths; neither is the angle through which the cover is opened 
represented in its actual size. 

The corners of the cover must then be determined by co¬ 
ordinates from an end view of the box and cover. As the end of 
the cover is in the same plane as the end of the box, the simple 







MECHANICAL DRAWING 


111 


end view as shown in Fig. 59 will be sufficient. Extend the top of 
the box to the right, and from c and d let fall perpendiculars or 
a b produced, giving the points e and f. The point c may be 
located by means of the two distances or co-ordinates 5 e and e c- 



and these distances will appear in their true lengths in the 
isometric view. Hence produce a* V to e’ and f ; and from these 
points draw verticals e' c' and/*' d r ; make V e’ equal to b e, e f c f 
equal to e c; and similarly for d'. Draw the lower edge parallel 
to c' d ' and equal to it in length, and 
connect with l >'. 

It will be seen that in isometric draw¬ 
ing parallel lines always appear parallel. 

It is also true that lines divided propor¬ 
tionally maintain this same relation in 
isometric drawing. 

Fig. 60 shows a block or prism with a 
semicircular top. Find the isometric of 
the square circumscribing the circle, then 
draw the curve by the approximate method. 

The centers for the back face are found 
by projecting the front centers back 30° 
equal to the thickness of the prism, as 
shown at a and b. The plan and elevation of an oblique pentagonal 
pyramid are shown in Fig. 61. It is evident that none of the 
edges of the pyramid can be drawn in isometric as either vertical 
or 30° lines; hence, a system of co-ordinates must be used as 



Fig. 60. 











112 


MECHANICAL DRAWING 


shown in Fig. 58. This problem illustrates the most general case; 
and to locate some of the points three co-ordinates must be used, 
two at 80° and one vertical. 

Circumscribe, about the plan of the pyramid, a rectangle which 
shall have its sides respectively parallel and perpendicular to the 
ground line. This rectangle is on H, and its vertical projection is 
in the ground line. 

The isometric of this rectangle can be drawn at once with 80° 
lines, as shown in Fig. G2, o being the same point in both figures. 



•77 

Fig. 61. 


The horizontal projection of point 3 is found in isometric at 8 h , at 
the same distance from o as in the plan. That is, any distance 
which in plan is parallel to a side of the circumscribing rectangle, * 
is shown in isometric in its true length and parallel to the corre¬ 
sponding side of the isometric rectangle. If point 8 were on the 
horizontal plane its isometric would be 8 h , but the point is at the 
vertical height above II given in the elevation; hence, lay off above 
8 h this vertical height, obtaining the actual isometric of the point. 
To locate 4, draw 4 a parallel to the side of the rectangle; then lay 















MECHANICAL DRAWING 


113 


off o a and a 4 h , giving what may be called the isometric plan of 4 
Next, the vertical height taken from the elevation locates the iso¬ 
metric of the point in space. 

In like manner all the 
corners of the pyramid, irn 
eluding the apex, are located. 

The rule is, locate first in 
isometric the horizontal 'pro¬ 
jection of a point by one or 
two 30° co-ordinates; then 
vertically , above this point , 
its height as taken from 
the elevation. The shade 
lines cannot be determined 
here by applying the 30° or 
60° triangle, owing to the 
obliquity of the faces. Since 
the right front corner of the 
rectangle in plan was made the point o in isometric, the shade 
lines must be the same in isometric as in actual projection; so that, 

if these can be de¬ 
termined in Fig. 61, 
they may be applied 
at once to Fig. 62. 

The shade lines 
in Fig. 61 are found 
by a short method 
which is convenient 
to use when the exact 
shade lines are de¬ 
sired, and when they 
cannot be deter¬ 
mined by applying 
the 45° triangle. A 
plane is taken at 45° 
with the horizontal 
plane, and parallel to the direction of the ray of light, in such a 
position as to cut all the surfaces of the pyramid, as shown in 



























114 


MECHANICAL DRAWING 


elevation. This plane is perpendicular to the vertical plane; hence 
the section it cuts from the pyramid is readily found in plan by 
projection. This plane contains some of the rays of light falling 
upon the pyramid; and we can tell what surfaces these rays strike 




and make light, by noticing on the plan what edges of the section are 
struck by the projections of the rays of light. That is, rs,st , and t u 
receive the rays of light; hence the surfaces on which these lines lie 
are light, r s is on the surface determined by the two lines passing 



































MECHANICAL DRAWING 


115 


through r and s, namely, 2 — 1 and 1 — 5; in other words, r s is 
on the base; similarly, s t is on the surface 1 — 5 — 6; and ^on 
the surface 4 — 6 — 5. The other surfaces are dark; hence the edges 
which are between the light and dark faces are the shade lines. 

Whenever it is more convenient, a plane parallel to the ray 
of light and perpendicular to H may be taken, the section found 
in elevation, and the 45° triangle applied to this section. The 
same method may be used to determine the exact shade lines 
of a cone or cylinder in an oblique position. 

Figs. 63 to 70 give examples of the isometric of various 
objects. Fig. 65 is the plan and elevation, and Fig. 66 the 



isometric, of a carpenter’s bench. In Fig. 70, take especial notice 
of the shade lines. These are put on as if the group were made 
in one piece; and the shadows cast by the blocks on one another 
are disregarded. All upper horizontal faces are light, all left-hand 
(front and back) faces light, and the rest dark. 

OBLIQUE PROJECTIONS. 

In oblique projection, as in isometric, the end sought for is 
the same—a more or less complete representation, in one view, of 
any object. Oblique projection differs from isometric in that one 
face of the object is represented as if parallel to the vertical 
plane of projection, the others inclined to it. Another point of 








116 


MECHANICAL DRAWING 


difference is that oblique projection cannot be deduced from 
orthographic projection, as is isometric. 

In oblique projection all lines in the front face are shown in 
their true lengths and in their true relation to one another, and 
lines which are perpendicular to this front face are showm in their 
true lengths at any angle that may be desired for any particular 
case. Lines not in the plane of the front face nor perpendicular 




to it must be determined by co-ordinates, as in isometric. It will 
be seen at once that this system possesses some advantages over 
the isometric, as, for instance, in the representation of circles, 




as any circle or curve in the front face is actually drawn as such. 

The rays of light are still supposed to be parallel to the same 
diagonal of the cube, that is, sloping downward, toward the plane 
of projection, and to the right, or downward, backward and to 
the right. Figs. 71, 72 and 73 show a cube in oblique projection, 













MECHANICAL DRAWING 


117 


with the 30°, 45° and 60° slant respectively. The dotted diagonal 
represents for each case the direction of the light, and the shade 
lines follow from this. 

The shade lines have the same general position as in isometric 




drawing, the top, front and left-hand faces being light. No matter 
what angle may be used for the edges that are perpendicular to 
the front face, the projection of the diagonal of the cube on this 
face is always a 45° line; hence, for determining the shade lines on 



any front face, such as the end of the hollow cylinder in Fig. 74, 
the 45° line is used exactly as in the elevation of ordinary 
projections. 

Figs. 75, 76, 77 and 79 are other examples of oblique projections. 
Fig. 77 is a crank arm. 

The method of* using co-ordinates for lines of which the true 














118 


MECHANICAL DRAWING 


lengths are not shown, is illustrated by Figs. 78 and 79. Fig. 79 
represents the oblique projection of the two joists shown in plan 
and elevation in Fig. 78. The dotted lines in the elevation (see 
Fig. 78) show the heights of the corners above the horizontal 
stick. The feet of these perpendiculars give the horizontal dis¬ 
tances of the top corners from the end of the horizontal piece. 

In Fig. 79 lay off from the upper right-hand corner of the 
front end a distance equal to the distance between the front edge 
of the inclined piece and the front edge of the bottom piece (see 
Fig. 78). From this point draw a dotted line parallel to the 



Fig. 78. 


length. The horizontal distances from the upper left corner to 
the dotted perpendicular are then marked off on this line. From 
these points verticals are drawn, and made equal in length to the 
dotted perpendiculars of Fig. 78, thus locating two corners of the 
end. 

LINE SHADING. 

In finely finished drawings it is frequently desirable to make 
the various parts more readily seen by showing the graduations of 
light and shade on the curved surfaces. This is especially true of 
such surfaces as cylinders, cones and spheres. The effect is 
obtained by drawing a series of parallel or converging lines on 
the surface at varying distances from one another. Sometimes 
draftsmen vary the wddth of the lines themselves. These lines are 
farther apart on the lighter portion of the surface, and are closer 
together and heavier on the darker part. 














MECHANICAL DRAWING 


11 <J 


Fig. 80 shows a cylinder with elements drawn on the surface 
equally spaced, as on the plan. On account of the curvature of 
the surface the elements are not equally spaced on the elevation, 
but give the effect of graduation of light. The 
result is that in elevation the distances between 
the elements gradually lessen from the center 
toward each side, thus showing that the cylinder 
is convex. The effect is intensified, however, if 
the elements are made heavier, as well as closer 
together, as shown in Figs. 81 to 87. 

Cylinders are often shaded with the light 
coming in the usual way, the darkest part com¬ 
mencing about where the shade line would actually 
be on the surface, and the lightest portion a little 
to the left of the center. Fig. 81 is a cylinder 
showing the heaviest shade at the right, as this 
method is often used. Considerable practice is 
necessary in order to obtain good results; but in 
this, as in other portions of mechanical drawing, 
perseverance has its reward. Fig. 82 represents a cylinder in a 
horizontal position, and Fig. 83 represents a section of a hollow 



Fig. 80. 



Fig. 81. 


Fig. 82. 


Fig. 83. 


Figs. 84 to 87 give other examples of familiar objects. 

In the elevation of the cone shown in Fig. 87 the shade lines 
should diminish in weight as they approach the apex. Unless 
this is done it will be difficult to avoid the formation of a blot at 
that point. 






























































120 


MECHANICAL DKAWING 


LETTERING. 

All working drawings require more or less lettering, such as 
titles, dimensions, explanations, etc. In order that the drawing 
may appear finished, the lettering must be well done. No style 
of lettering -should ever be used which is not perfectly legible. 
It is generally best to use plain, easily-made letters which present 


Fig. 84. 





Fig. 86. 



Fig. 87. 


a neat appearance. Small letters used on the drawing for notes or 
directions should be made free-hand with an ordinary writing pen. 
Two horizontal guide lines should be used to limit the height of 
the letters; after a time, however, the upper guide line may be 
omitted. 























MECHANICAL DRAWING 


121 


In the early part of this course the inclined Gothic letter was 
described, and the alphabet given. The Roman, Gothic and block 
letters are perhaps the most used for titles. These letters, being 
of comparatively large size, are generally made mechanically; that 
is, drawing instruments are used in their construction. In order 
that the letters may appear of the same height, some of them, 
owing to their shape, must be made a little higher than the others. 
This is the case with the letters curved at the top and bottom, 
such as C, O, S, etc., as shown somewhat exaggerated in 
Fig. 88. Also, the letter A should extend a little above, and V a 
little below, the guide lines, because if made of the same height 
as the others they will appear shorter. This is true of all capitals, 
whether of Roman, Gothic, or other alphabets. In the block letter, 
however, they are frequently all of the same size. 

There is no absolute size or proportion of letters, as the 
dimensions are regulated by the amount of space in which the 
letters are to be placed, the size of the drawing, the effect desired, 
etc. In some cases letters are made so that the height is greater 
than the width, and sometimes the reverse; sometimes the height 
and width are the same. This last proportion is the most common. 
Certain relations of width, however, should be observed. Thus, in 
whatever style of alphabet used, the W should be the widest letter; 
J the narrowest, M and T next widest to W, then A and B. The 
other letters are of about the same width. 

In the vertical Gothic alphabet, the average height is that of 
B, D, E, F, etc., and the additional height of the curved letters 
and of the A and V is very slight. The horizontal cross lines of 
such letters as E, F, H, etc., are slightly above the center; those 
of A, G and P slightly below. 

For the inclined letters, 60° is a convenient angle, althoiigh 
they may be at any other angle suited to the convenience or fancy 
of the draftsman. Many draftsmen use an angle of about 70°. 

The letters of the Roman alphabet, whether vertical or 
inclined, are quite ornamental in effect if well made, the inclined 
Roman being a particularly attractive letter, although rather 
difficult to make. The block letter is made on the same general 
plan as the Gothic, but much heavier. Small squares are taken as 




122 


MECHANICAL DRAWING. 



Inclined Gothic Capitals- 



MECHANICAL DRAWING 


123 


the unit of measurement, as shown. The use of this letter is not 
advocated for general work, although if made merely in outline the 
effect is pleasing. The styles of numbers corresponding with 
the alphabets of capitals given here, are also inserted. When a 
fraction, such as 2§ is to be made, the proportion should be about 
as shown. For small letters, usually called lower-case letters, 

a bcdefg h ij kl m n 
opqrstuvwxyz 

Fig. 89. 

abcc/ef'gh/Jk/mn 
opqtrs tuv wjcjsz 

Fig. 90. 

abcdefghijklmn 

opqrstuvwxyz 

Fig. 91. 

the height may be made about two-thirds that of the capitals. 
This proportion, however, varies in special cases. 

The principal lower-case letters in general use among drafts¬ 
men are shown in Figs. 89, 90, 91 and 92. The Gothic letters 
shown in Figs. 89 and 90 are much easier to make than the 
Roman letters in Figs. 91 and 92. These letters, however, do not 



124 


MECHANICAL DRAWING. 



Inclined Roman Capitals. 



MECHANICAL DRAWING 


125 ' 


give as finished an appearance as the Roman. As has already 
been stated in Mechanical Drawing, Part I, the inclined letter is 
easier to make because slight errors are not so apparent. 

One of the most important points to be remembered in letter¬ 
ing is the spacing. If the letters are finely executed but poorly 
spaced, the effect is not good. To space letters correctly and 
rapidly, requires considerable experience; and rules are of little 
value on account of the many combinations in which letters are 

ab c defg hijkLrrzn 
opq ns tuvwxy z 

Fig. 92. 

found. A few directions, however, may be found helpful. For 
instance, take the word TECHNICALITY, Fig. 93. If all the 
spaces were made equal, the space between the L and the I would 
appear to be too great, and the. same would apply to the space 
between the I and the T. The space between the H and the N 
and that between the N and the I would be insufficient. In 
general, when the vertical side of one letter is followed by the verti¬ 
cal side of another, as in H E, H B, I R, etc., the maximum space 

TECHNICALITY 

Fig. 93. 


should be allowed. Where T and A come together the least space 
is given, for in this case the top of the T frequently extends over 
the bottom of the A. In general, the spacing should be such that 
a uniform appearance is obtained. For the distances between 
words in a sentence, a space of about 1| the width of the average 
letter may be used. The space, however, depends largely upon the 
desired effect. 



126 


MECHANICAL DRAWING 


For large titles, such as those placed on charts, maps, and 
some large working drawings, the letters should be penciled before 
inking. If the height is made equal to the width considerable 
time and labor will be saved in laying out the work. This is 
especially true with such Gothic letters as O, Q, C, etc., as these 
letters may then be made with compasses. If the letters are of 
sufficient size, the outlines may be drawn with the ruling pen or 
compasses, and the spaces between filled in with a fine brush. 

The titles for working drawings are generally placed in the 
lower right-hand corner. Usual a draftsman has his choice of 




Block Letters. 


letters, mainly because after he has become used to making one 
style he can do it rapidly and accurately. However, in some draft¬ 
ing rooms the head draftsman decides wffiat lettering shall be used. 
In making these titles, the different alphabets are selected to give 
' the best results without spending too much time. In most work 
the letters are made in straight lines, although we frequently find 
a portion of the title lettered on an arc of a circle. 

In Fig. 94 is shown a title having the words CONNECTING 
ROD lettered on an arc of a circle. To do this work requires 
considerable patience and practice. First draw the vertical center 













































































































































































































MECHANICAL DRAWING 


127 


line as shown at C in Fig. 94. Then draw horizontal lines for the 
horizontal letters. The radii of the arcs depend upon the general 
arrangement of the entire title, and this is a matter of taste. The 
difference between the arcs should equal the height of the letters. 
After the arc is drawn, the letters should be sketched in pencil to 
find their approximate positions. After this is done, draw radial 
lines from the center of the letters to the center of the arcs. 



BEAM ENGINE 

SCALE 3 INCHES = 1 FOOT 


PORTLAND COMPANY’S WORKS 

JULY 10, 1804- 

Pig. 94. 


These lines will be the centers of the letters, as shown at A, B, D 
and E. The vertical lines of the letters should not radiate from 
the center of the arc, but should be parallel to the center lines 
already drawn; otherwise the letters will appear distorted. Thus, 
in the letter N the two verticals are parallel to the line A. The 
same applies to the other letters in the alphabet. 




128 


MECHANICAL DRAWING 


Tracing. Having finished the pencil drawing, the next step 
is the inking. In some offices the pencil drawing is made on a thin, 
tough paper, called board paper, and the inking is done over the 
pencil drawing, in the manner with which the student is already 
familiar. It is more common to do the inking on thin, trans¬ 
parent cloth, called tracing cloth, which is prepared for the pur¬ 
pose. This tracing cloth is made of various kinds, the kind in 
ordinary use being what is known as “ dull back,” that is, one 
side is finished and the other side is left dull. Either side may 
be used to draw upon, but most draftsmen prefer the dull side. 
If a drawing is to be traced it is a good plan to use a 3H or 4H 
pencil, so that the lines may be easily seen through the cloth. 

The tracing cloth is stretched smoothly over the pencil draw¬ 
ing and a little powdered chalk rubbed over it with a dry cloth, 
to remove the slight amount of grease or oil from the surface and 
make it take the ink better. The dust must be carefully brushed 
or wiped off with a soft cloth, after the rubbing, or it w T ill inter¬ 
fere with the inking;. 

The drawing is then made in ink on the tracing cloth, after 
the same general rules as for inking the paper, but xjare must be 
taken to draw the ink lines exactly over the pencil lines which 
are on the paper underneath, and which should be just heavy 
enough to be easily seen through the tracing cloth. The ink lines 
should be firm and fully as heavy as for ordinary work. In tracing, 
it is better to complete one view at a time, because if parts of 
several views are traced and the drawing left for a day or two, the 
cloth is liable to stretch and warp so that it will be difficult to 
complete the views and make the new lines fit those already 
drawn and at the same time conform to the pencil lines under¬ 
neath. For this reason it is well, when possible, to complete a 
view before leaving the drawing for any length of time, although 
of course on views, in which there is a good deal of work this 
cannot always be done. In this case the draftsman must manipu¬ 
late his tracing cloth and instruments to make the lines fit as best 
he can. A skillful draftsman will have no trouble from this 
source, but the beginner may at first find difficulty. 

Inking on tracing cloth will be found by the beginner to be 
quite different from inking on the paper to which he has been 
accustomed, and he will doubtless make many blots and think ai 



MECHANICAL DKAWING 


129 


first that it is hard to make a tracing. After a little practice, 
nowever, he will find that the tracing cloth is very satisfactory 
and that a good drawing can be made on it quite as easily as on 
paper. 

The necessity for making erasures should be avoided, as far 
as possible, but when an erasure must be made a good ink rubber 
or typewriter eraser may be used. If the erased line is to have 
ink placed on it, such as a line crossing, it is better to use a soft 
rubber eraser. All moisture should be kept from the cloth. 

Blue Printing, The tracing, of course, cannot be sent into 
the shop for the workmen to use, as it would soon become soiled 
and in time destroyed, so that it is necessary to have some cheap 
and rapid means of making copies from it. These copies are 
made by the process of blue printing in which the tracing is used 
in a manner similar to the use made of a negative in photography. 

Almost all drafting rooms have a frame for the purpose of 
making blue prints. These frames are made in many styles, some 
simple, some elaborate. A simple and efficient form is a flat sur¬ 
face usually of wood, covered with padding of soft material, such 
as felting. To this is hinged the cover, which consists of a frame 
similar to a picture frame, in which is set a piece of clear glass. 
The whole is either mounted on a track or on some sort of a 
swinging arm, so that it may readily be run in and out of a 
window. 

The print is made on paper prepared for the purpose by 
having one of its surfaces coated with chemicals which are sensi¬ 
tive to sunlight. This coated paper, or blue-print paper, as it is 
called, is laid on the padded surface of the frame with its coated 
side uppermost; the tracing laid over it right side up, and the 
glass pressed down firmly and fastened in place. Springs are 
frequently used to keep the paper, tracing, etc., against the glass. 
With some frames it is more convenient to turn them over and 
remove the backs. In such cases the tracing is laid against the 
glass, face down; the coated paper is then placed on it with the 
coated side against the tracing cloth. 

The sun is allowed to shine upon the drawing for a few 
minutes, then the blue-print paper is taken out and thoroughly 
washed in clean water for several minutes and hung up to dry. 



130 


MECHANICAL DRAWING 


If the paper has been recently prepared and the exposure properly 
timed, the coated surface of the paper will now be of a clear, deep 
blue color, except where it was covered by the ink lines, where it 
will be perfectly white. 

The action has been this: Before the paper was exposed to 
the light the coating was of a pale yellow color, and if it had then 
been put in water the coating would have all washed off, leaving 
the paper white. In other words, before being exposed to the 
sunlight the coating was soluble. The light penetrated the trans¬ 
parent tracing cloth and acted upon the chemicals of the coating, 
changing their nature so that they became insoluble; that is, when 
put in water, the coating, instead of being washed off, merely 
turned blue. The light could not penetrate the ink with which 
the lines, figures, etc., were drawn, consequently the coating under 
these was not acted upon and it washed off when put in water, 
leaving a white copy of the ink drawing on a blue background. 
If running water cannot be used, the paper must be washed in a 
sufficient number of changes until the water is clear. It is a good 
plan to arrange a tank having an overflow, so that the water may 
remain at a depth of about 6 or 8 inches. 

The length of time to which a print should be exposed to the 
light depends upon the quality and freshness of the paper, the 
chemicals used and the brightness of the light. Some paper is 
prepared so that an exposure of one minute, or even less, in bright 
sunlight, will give a good print and the time ranges from this to 
twenty minutes or more, according to the proportions of the 
various chemicals in the coating. If the full strength of the sun¬ 
light does not strike the paper, as, for instance, if clouds partly 
cover the sun, the time of exposure must be lengthened.' 

Assembly Drawing. We have followed through the process 
of making a detail drawing from the sketches to the blue print 
ready for the workmen. Such a detail drawing or set of drawings 
shows the form and size of each piece, but does not show how the 
pieces go together and gives no idea of the machine as a w T hole. 
Consequently, a general drawing or assembly drawing must be 
made, which will show these things. Usually two or more views 
are necessary, the number depending upon the complexity of the 
machine. Very often a cross-section through some part of the 



MECHANICAL DRAWING 


131 


machine, chosen so as to give the best general idea with the least 
amount of work, will make the drawing clearer. 

The number of dimensions required on an assembly drawing 
depends largely upon the kind of machine. It is usually best to 
give the important over-all dimensions and the distance between 
the principal center lines. Care must be taken that the over-all 
dimensions agree with the sum of the dimensions of the various 
details. For example, suppose three pieces are bolted together, 
the thickness of the pieces according to the detail drawing, being 
one inch, two inches, and five and one-lialf inches respectively; the 
sum of these three dimensions is eight and one-half inches and 
the dimensions from outside on the assembly drawing, if given at 
all, must agree with this. It is a good plan to add these over-all 
dimensions, as it serves as a check and relieves the mechanic of the 
necessity of adding fractions. 


FORMULA FOR BLUE=PRINT SOLUTION. 

Dissolve thoroughly and filter. 


Red Prussiate of potash.ounces, 

A ' Water...1 pint, 

Ammonio-Citrate of iron.4 ounces, 

B ' Water.1 pint. 

Use equal parts of A and B. 


FORHULA FOR BLACK PRINTS 


Negatives. White lines on blue ground; prepare the paper 


with 

Ammonio-Citrate of iron.40 grains, 

Water. 1 ounce. 


After printing wash in water. 

Positives. Black lines on white ground; prepare the paper 
with: 

Iron perchloride.. ..616 grains, 

Oxalic Acid... 308 grains, 

Water. 14 ounces. 


T Gallic Acid. 1 ounce, 

Develop in -j Citric Acid. 1 ounce, 

(Alum.. 8 ounces. 


Use 1J ounces of developer to one gallon of water. Paper is 
fully exposed when it has changed from yellow to white. 















132 


MECHANICAL DRAWING 


PLATES. 

PLATE IX. 

The plates of this Instruction Paper should be laid out at the 
same size as the plates in Parts I and II. The center lines and 
border lines should also be drawn as described. 

First draw two ground lines across the sheet, 3 inches below 
the upper border line and 3 inches above the lower border line. 
The first problem on each ground line is to be placed 1 inch from 
the left border line; and spaces of about 1 inch should be left 
between the figures. 

Isolated points are indicated by a small cross X, and projections 
of lines are to be drawn full unless invisible. All construction 
lines should be fine dotted lines. Given and required lines should 
be drawn full. 

Problems on Upper Ground Line: 

1. Locate both projections of a point on the horizontal plane 
1 inch from the vertical plane. 

2. Draw the projections of a line 2 inches long which is 
parallel to the vertical plane and which makes an angle of 45 
degrees with the horizontal plane and slants upward to the right. 

The line should be 1 inch from the vertical plane and the lower end 
% inch above the horizontal. 

3 Draw the projections of a line 1| inches long which is 
parallel to both planes, 1 inch above the horizontal, and f inch from 
the vertical. 

4. Draw the plan ana elevation of a line 2 incnes long which 
is parallel to H and makes an angle of 30 degrees with V. Let the 
right-hand end of the line be the end nearer V, \ inch from V. 
The line to be 1 inch above H. 

5. Draw the plan and elevation of a line 1J inches long 
which is perpendicular to the horizontal plane and 1 inch from the 
vertical. Lower end of line is ^ inch above H. 

6. Draw the projections of a line 1 inch long which is 
perpendicular to the vertical plane and 1| inches above the 
horizontal. The end of the line nearer V, or the back end, is 
| inch from V. 




EEBRUARY /7, /SO7 HERBERT CHANDLER y CH/CAGO, /LL. 






































































































FEBRUARY' SO, /907 HERBERT CHANDLER CHICAGO, /LL. 


































































































MECHANICAL DRAWING 


133 


7. Draw two projections which shall represent a line oblique 
to both planes. 

Note. Leave 1 inch between this figure and the right-hand border line. 
Problems on Lower Ground Line: 

8. Draw the projections of two parallel lines each inches 
long. The lines are to be parallel to the vertical plane and to make 
angles of 60 degrees with the horizontal. The lower end of each 
line is £ inch above H. The right-hand end of the right-hand line 
is to be 2£ inches from the left-hand margin. 

9. Draw the projections of two parallel lines each 2 inches 
long. Both lines to bo parallel to the horizontal and to make 
an angle of 30 degrees with the vertical. The lower line to be 
£ inch above H, and one end of one line to be against V. 

10. Draw the projections of two intersecting lines. One 
2 inches long to be parallel to both planes, 1 inch above H, and 
£ inch from the vertical; and the other to be oblique to both 
planes and of any desired length. 

11. Draw plan and elevation of a prism 1 inch square and 1£ 
inches long. The prism to have one side on the horizontal plane, 
and its long edges to be perpendicular to V. The back end of the 
prism is \ inch from the vertical plane. 

12. Draw plan and elevation of a prism the same size as given 
above, but with the long edges parallel to both planes, the lower 
face of the prism to be parallel to H and £ inch above it, The 
back face to be £ inch from V. 

PLATE X. 

The ground line is to be in the middle of the sheet, and the 
location and dimensions of the figures are to be as given. The 
first figure shows a rectangular block with a rectangular hole cut 
through from front to back. The other two figures represent the 
same block in different positions. The second figure is the end or 
profile projection of the block. The same face is on H in all 
three positions. Be careful not to omit the shade lines. The 
figures given on the plate for dimensions, etc., are to be used but 
not repeated on the plate by the student. 




134 


MECHANICAL DRAWING 


PLATE XI. 

Three ground lines are to be used on this plate, two at the left 
4^ inches long and 3 inches from top and bottom margin lines; and 
one at the right, half way between the top and bottom margins, 9^ 
inches long. 

The figures 1, 2, 3 and 4 are examples for finding the true 
lengths of the lines. Begin No. 1 finch from the border, the 
vertical projection If inches long, one end on the ground line and 
inclined at 30°. The horizontal projection has one end ^ incl 
from V, and the other 1J inches from V. Find the true length of 
the line by completing the construction commenced by swinging 
the arc, as shown in the figure. 

Locate the left-hand end of No. 2 3 inches from the border, 
1 inch above H, and § inch from V. Extend the vertical projection 
to the ground line at an angle of .45°, and make the horizontal pro¬ 
jection at 30°. Complete the construction for true length as 
commenced in the figure. 

In Figs. 3 and 4, the true lengths are to be found by complet¬ 
ing the revolutions indicated. The left-hand end of Fig. 3 is f 
inch from the margin, 1| inches from V, and If inches above H. 
The horizontal projection makes an angle of 60° and extends to the 
ground line, and the vertical projection is inclined at 45°. 

The fourth figure is 3 inches from the border, and represents 
a line in a profile plane connecting points a and l. a is If inches 
above H and f inch from V; and b is \ inch above H and 1| 
inches from V. 

The figures for the middle ground line represent a pentagonal 
pyramid in three positions. The first position is the pyramid with 
the axis vertical, and the base § inch above the horizontal. The 
height of the pyramid is 2J inches, and the diameter of the circle 
circumscribed about the base is 2J inches. The center of the circle 
is 6 inches from the left margin and If inches from V. Spaces 
between figures to be f inch. 

In the second figure the pyramid has been revolved about the 
right-hand corner of the base as an axis, through an angle of 15°. 
The axis of the pyramid, shown dotted, is therefore at 75°. The 
method of obtaining 75° and 15° with the triangles was shown in 



PLATE 




r 


i 

i 







PRBPUAP Y 27, /907 PEP SEPT CHANDLER CH/CACO, /LL 


































































































MECHANICAL DRAWING 


135 


Part I. From the way in which the pyramid has been revolved, 
all angles with V must remain the same as in the first position. 
hence the vertical projection will be the same shape and size as 
before. All points of the pyramid remain the same distance 
from V. The points on the plan are found on T-square lines 
through the corners of the first plan and directly beneath the 
points in elevation. In the third position the pyramid has been 
swung around, about a vertical line through the apex as axis, 
through 30°. The angle with the horizontal plane remains the 
same; consequently the plan is the same size and shape as in the 


A 



Pig. 96. 


second position, but at a different angle with the ground line. 
Heights of all points of the pyramid have not changed this time, 
and hence are projected across from the second elevation. Shade 
lines are to be put on between the light and dark surfaces as 
determined by the 45° triangle. 

PLATE XU. 

Developments. 

On this plate draw the developments of a truncated octagonal 
prism, and of a truncated pyramid having a square base. The 
arrangement on the plate is left to the student; but we should 
suggest that the truncated prism and its development be placed at 





























136 


. MECHANICAL DRAWING 


the left, and that the development of the truncated pyramid be 
placed under the development of the prism; the truncated pyramid 
may be placed at the right. 

The prism and its development are shown in Fig. 96. The 
prism is 3 inches high, and the base is inscribed in a circle 2J 
inches in diameter. The plane forming the truncated prism is 
passed as indicated, the distance A B being 1 inch. Ink a suffi¬ 
cient number of construction lines to show clearly the method of 
finding the development. 

The pyramid and its development are shown in Fig. 97. Each 
side of the square base is 2 inches, and the altitude is 3J inches. 


A 



Fig. 97. 


The plane forming the truncated pyramid is passed in such a 
position that A B equals If inches, and A C equals 2J inches. In 
this figure the development may be drawn in any convenient 
position, but in the case of the prism it is better to draw the 
development as shown. Indicate clearly the construction by 
inking the construction lines. 

PLATE XIII. 

Isometric and Oblique Projection. 

Draw the oblique projection of a portable closet. The angle to 
be used is 45°. Make the height 3J inches, the depth 1J inches, 
and the width 3 inches. See Fig. 98. The width of the closet 














MARCH V, /9Q7 HERBERT CHANDLER CH/CAGO, /LL. 




























































































































































MECHANICAL DRAWING 


137 


is to be shown as the left-hand face. The front left-hand lower 
corner is to be 1 inch from the left-hand border line and 2 inches 
from the lower border line. The door to be placed in the closet 
should be 1§ inches wide and 2f inches high. Place the door 



centrally in the front of the closet, the bottom edge at the height 
of the floor of the closet, the hinges of the door to be placed on the 
left-hand side. In the oblique drawing, show the door opened 
at an angle of 90 degrees. The thickness of the material of the 
closet, door, and floor is ^ inch. 

The door should be hung so that 
when closed it will be flush with 
the front of the closet. 

Make the isometric drawing 
otthe flight of steps andendwalls 
as shown by the end view in Fig. 

99. The lower right-hand corner 
is to be located 2\ inches from 
the lower, and 5 inches from the 
right-hand, margin. The base of the end wall is 3J inches Jong, 
and the height is 2\ inches. Beginning from the back of the 
wall, the top is horizontal for § inch, the remainder of the outline 
being composed of arcs of circles whose radii and centers are given 




























138 


MECHANICAL DRAWING 


in the figure. The thickness of the end wall is f inch, and both 
ends are alike. There are to be five steps; each rise is to be 
f inch, and each tread f inch, except that of the top step, which 
is | inch. The first step is located § inch back from the corner 
of the wall. Tire end view of the wall should be constructed on a 
separate sheet of paper, from the dimensions given, the points on 
the curve being located by horizontal co-ordinates from the vertical 
edge of the wall, and then these co-ordinates transferred to the 
isometric drawing. After the isometric of one curved edge has 
been made, the others can be readily found from this. The width 
of the steps inside the walls is 3 inches. 

PLATE XIV. 

Free=hand Lettering. 

On account of the importance of free-hand lettering, the 
student should practice it at every opportunity. For additional 
practice, and to show the improvement made since completing 
Part I, lay out Plate XIV in the same manner as Plate I, and letter 
all four rectangles. Use the same letters and words as in the lower 
light-hand rectangle of Plate I. 

PLATE XV. 

Lettering. 

First lay out Plate XV in the same manner as previous 
plates. After drawing the vertical center line, draw light pencil 
lines as guide lines for the letters. The height of each line of 
letters is shown on the reproduced plate. The distance be¬ 
tween the letters should be J inch in every case. The spacing 
of the letters is left to the student. He may facilitate his work 
by lettering the words on a separate piece of paper, and finding 
the center by measurement or by doubling the paper into two 
equal parts. The styles of letters shown on the reproduced plate 
should be used 



PLATE 



APP/L 2 A. /907 PEP SEPT CHANDLER CH/CAGO. /LL 











INDEX 


Page 

Acute angle. 40 

Altitude of triangle. 41 

Angles. 40 

measurement of. 44 

Assembly drawing. 130 

Base of triangle. 41 

Beam compasses. 21 

Black prints, formula for. 131 

Blue-print solution, formula for. 131 

Blueprinting. 129 

Bow pen.*.... 1G 

Bow pencil... 16 

Broken line. 39 

Central angle. 44 

Chord. 43 

Circles. 43 

Circumference of a circle. 43 

Compasses....'. 12 

Concentric circle. 44 

Cones. 47 

Conic sections. 49 

Conical surface.*. 47 

Cube. 46 

Curved line. 39 

Cycloid. 51 

Cylinders. 47 

Decagon. 42 

Development. 85 

of cylinder.. 95 

frustrum of the cone. 93 

rectangular prism... 91 

right prism. 91 

Diagonal of quadrilateral. 41 

Diameter of a circle. 43 

Dividers. 15 

Dodecagon. 42 

Drawing board.. • • .. 5 

Drawing paper. 3 

Drawing pen. 16 

to sharpen. 17 












































140 


INDEX 


Page 

Ellipse. 49 

Epicycloid. 52 

Erasers..... Q, 

Foci. 49 

Frustum of a cone. 48 

Frustum of a pyramid. 47 

Geometrical definitions. 39 

angles. 40 

circles. 43 

cones. 47 

conic sections. 49 

cylinders. 47 

odontoidal curves.. 51 

polygons... 42 

pyramids. 46 

quadrilaterals. 41 

solids. 45 

spheres. 48 

surfaces. 40 

triangles. 40 

Geometrical problems. 53 

Gothic capitals. 22 

Heptagon. 42 

Hexagon. 42 

Horizontal line... 39 

Hyperbola. 50 

Hypocycloid. 52 

Ink. 18 

Inscribed angle. 44 

Inscribed polygon.- 44 

Instruments. 3 

beam compasses. 21 

bow pen. 16 

bow pencil. 16 

compasses...-. 12 

dividers. 15 

drawing board. 5 

drawing pen. 16 

erasers.. 6 

irregular curve. 20 

pencils. 6 

protractor. 19 

scales. 19 

T-square. 7 

thumb tacks. 5 

triangles. 9 

Intersection. 85 

of planes with cones or cylinders. 86 



















































INDEX 


141 


Page 

Involute. 52 

Irregular curve.;. 20 

Isometric axes. 105 

Isometric projection. 103 

Isosceles triangle. 41 

Lettering.21, 120 

Line, definition of. 39 

Line shading. 118 

Lower-case letters. 123 

Materials. 3 

drawing paper. 3 

ink. 18 

Oblique line. 39 

Oblique projections. 115 

Obtuse angle. 40 

Octagon. 42 

Odontoidal curves. 51 

Orthographic projection. 69 

Parabola. 50 

Parallel lines. 39 

Parallelogram. 42 

Parallelopiped. 46 

Pencils. 6 

Pentagon. 42 

Plane figure. 40 

Plates.25, 53, 132 

Point, definition of. 39 

Polyedron. 45 

Polygons. 42 

Prism. 45 

Profile plane. 75 

Projections. 69 

isometric. 103 

oblique. 115 

orthographic.. 69 

third plane of. 75 

Protractor. 19 

Pyramids. 46 

Quadrilaterals.. 41 

Radius of a circle. 43 

Rectangle. 42 

Rectangular hyperbola. 51 

Rhomboid. 42 

Rhombus. 42 

Right angles. 40 

Scalene triangle. 41 

Scales. . 19 

Secant. • . 43 



















































Page 

Sector of a circle.. 44 

Segment of a circle. 44 

Shade lines. 81 

Solids. 45 

Spheres. 48 

Square. 42 

Straight line. 39 

Surfaces. .. . . . .. 40 

T-square. 7 

Tangent. 43 

Third plane of projection. 75 

Thumb tacks. 5 

Tracing...'. 128 

Trapezium. 41 

Trapezoid. 41 

Triangles. 40 

Truncated prism. 46 

Truncated pyramid. 47 

Vertical line. 39 

























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II ■tiwi— 


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